I think that it is not correct to say that "ancient hate the parallel postulate".
For sure, it is not so "self-evident" as others [but please, think at Common notion n°5 : "The whole is greater than the part"; until Cantor it was "absolutely" self-evident].
The possible explanation, as per Gerry's comment, is that it involves the infinite, and the infinite is not so easy to manage ...
According to Boris Rosenfeld, A History of Non-euclidean Geometry (original ed.1976), page 36, Euclid was "aware" of this :
Euclid tries to prove as many theorems as possible without using the fifth postulate. The first 28 propositions of Book I are so proved.
According to Rosenfeld [page 40] :
it seems that the first work devoted to this question was Archimedes' lost treatise On parallel lines that appeared a few decades after Euclid's Elements.
The title of this work in known only through the list of Archimedes' works by ibn al-Nadim (ca.990), and
it is possible that one of Ibn Qurra's preserved treatises on parallel lines represents an edited version of Archimedes' treatise.
[...] it is very likely that Archimedes used a definition of parallel lines different from Euclid's. [...] it is possible that Archimedes based his definition of parallel lines on distance.
Added
As finely remarked by mau, the original definition and postulate are [see Thomas Heath, The Thirteen Books of Euclid's Elements . Volume 1 : Introduction & Books I and II (1908 - Dover reprint) ] :
Def 23: Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.[page 154]
Postulate 5: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.[page 155]
Heath's edition comments at lenght definitions and postulates: the comment to P5 span from page 202 to page 220, with a lot of informations about the recorded attempt to prove it, from Proclus on.
Page 220 lists the most common alternatives to Euclid's version of the postulate; among them :
(I) Through a given point only one parallel can be drawn to a given straight line or, Two straight lines which intersect one another cannot both be parallel to one and the same straight line.
This is commonly known as "Playfair's Axiom" - from John Playfair (10 March 1748 – 20 July 1819) - , but it was of course not a new discovery. It is distinctly stated in Proclus' note to Eucl.I.31.
Here the list organised by main subject.
Add more if you know some, but add reference to where it comes from.
If a proposition falls under more than 2 subjects you may add them under both. Like triangle 5 ( Every triangle can be circumscribed ) and circle 1 ( Given any three points not on a straight line, there exists a circle through them).
Lines:
Euclid: If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. [1]
There is at most one line that can be drawn parallel to another given one through an external point. (Playfair's axiom)[1,6]
There exists a pair of straight lines that are at constant distance from each other.[1]
Two lines that are parallel to the same line are also parallel to each other.[1,6]
If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it also intersects the other. (Proclus' axiom) [1,6]
if two straight lines are parallel, they are figures opposite to (or the reflex of) one another with respect to the middle points of all their transversal arguments.(Veronese) [2]
Two parallel straight lines intercept, on every transversal which passes trough the middle point of a segment included between them, another segment the middle point of which is the middle of the first (Ingami) [2]
Two straight lines that intersect one another cannot be parallel to a third line. (no 7 at [3] )
If two lines are parallel , then alternate internal angles cut by an transversal are congruent (converse alternate internal angle theorem). [4,6]
If t is a transversal to $l$ and $ l \parallel m $ and $ t \bot l $ then $t \bot m $. [4,6]
if $ k \parallel l $ , $ m \bot k $ and $ m \bot l $ then either $ m=n $ or $ m \parallel n.$ [4]
Any two parallel lines have two common perpendicular lines. [5]
Any three distinct lines have a common transversal. [5]
There are not three lines such that any two of them are in the same side of the third. [5]
Two any parallel lines have a common perpendicular. [5]
Given $r,s$ lines, if $r$ is parallel to $s$, then $r$ is equidistant from $s$.[5]
Given a line $r$, the set of the points that are on the same side of $r$ and that are equidistant from $r$, is a line. [5]
Given lines $r,s,u,v$, if $r$ is parallel to $s$, $u$ is perpendicular to $r$ and $v$ is perpendicular to $s$, then $u$ and $v$ are parallel. [5,6]
Given lines $r,s,u,v$, if $r \perp s$, $s \perp u$ and $u \perp v$, then $r$ cuts $s$ (Bachmann Lottschnitt axiom). [5,6]
If $\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}$ and $\overleftrightarrow{BC}$ is transversal to both of them such that $A$ and $D$ are in the same side of $\overleftrightarrow{BC}$, then $m(\measuredangle ABC) + m(\measuredangle DCB) = 180°$. [5]
For any point P, line l, with P not incident with l, and any line g, there exists a point G on g for which the distance to P exceeds the distance to l [8]
Triangles:
The sum of the angles in every triangle is 180° (triangle postulate).[1,6]
There exists a triangle whose angles add up to 180°.[1,6]
The sum of the angles is the same for every triangle.[1]
There exists a pair of similar, but not congruent, triangles.[1,6]
Every triangle can be circumscribed.[1,6]
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (Pythagoras' Theorem).[1]
There is no upper limit to the area of a triangle. (Wallis axiom)[1]
Given a triangle $\Delta ABC$, if $(AC)^2 = (AB)^2 + (BC)^2$, then $\angle B$ is a right angle. (converse of Pythagorean Theorem) [5]
Given a triangle $\Delta ABC$, exists $\Delta DEF$ such that $A \in \overline{DE}$, $B \in \overline{EF}$ and $C \in \overline{FD}$. [5]
Given a triangle $\Delta ABC$, if $D$ and $E$ are respectively the middle points of $\overline{AB}$ and $\overline{AC}$, then $DE = \frac{1}{2}BC$. [5]
(Thales) Given a triangle $\Delta ABC$, with $B$ in the circle of diameter $\overline{AC}$, then $\angle ABC$ is a right angle. [5,6]
The perpendicular bisectors of the sides of a triangle are concurrent lines. [5,6]
Rectangles:
There exists a quadrilateral such that the sum of its angles is 360°. (answer Ivo Terek below)
If three angles of a quadrilateral are right angles, then the fourth angle is also a right angle.[1,6]
There exists a quadrilateral in which all angles are right angles.[1,6]
The summit angles of the Saccheri quadrilateral are 90°. [1,6]
If in a quadrilateral 3 angles are right angles, the fourth is a right angle also.[2,6]
Circles:
Given any three points not on a straight line, there exists a circle trough them. (Legendre, Bolay)[2,6]
A curve of constant non-zero curvature is a circle.
A curve of constant non-zero curvature has finite extent.
There exist circles of arbitrarily low curvature.
The area of a circle grows at most polynomially in its radius.
Other:
Through any point within an angle less than 60° a straight line can always be drawn which meet both sides of the angle. (Legendre)[2]
Given an angle $\angle ABC$ and $D$ in its interior, every line that passes throuh $D$ cuts $\overrightarrow{BA}$ or $\overrightarrow{BC}$. [5,6]
If $A,B$ and $C$ are points of a circle with center $D$ such that $B$ and $D$ are in the same side of $\overleftrightarrow{AC}$, then $m(\measuredangle ABC) = \frac{1}{2}m(\measuredangle ADC)$. [5]
Given a acute angle $\angle ABC$ and $D \in \overrightarrow{BA}$, $D \neq B$, if $t$ contains $D$ and is perpendicular to $\overleftrightarrow{AB}$, then $t$ cuts $\overrightarrow{BC}$. [5]
References:
[1]: wikipedia http://en.wikipedia.org/wiki/Parallel_postulate
[2]: Heath's "Euclid, The Thirteen Books of The Elements" Dover edition
[3]: cut the knot http://www.cut-the-knot.org/triangle/pythpar/Fifth.shtml
[4]: Greenberg's "Euclidean and Non-Euclidean geometries" 3rd edition 1994
[5]: Professor Sergio Alves' notes of Non-Euclidean Geometry, from University of São Paulo (the original notes (in portuguese) in three images: here, here and here)
[6]: The computer checked proofs of the equivalence between 34 statements:
http://geocoq.github.io/GeoCoq/html/GeoCoq.Meta_theory.Parallel_postulates.Euclid_def.html and the paper : https://hal.inria.fr/hal-01178236v2
[7]: Martin, The foundations of geometry and the non euclidean plane.
[8]: Pambuccian, Another equivalent of the Lotschnittaxiom, V. Beitr Algebra Geom (2017) 58: 167. doi:10.1007/s13366-016-0307-5
Best Answer
See Proclus' Commentary, Prop XXIX : Proclus' axiom is "proved" from a principle used by Aristotle [De Caelo, I] :
Then Proclus proves Euclid's Fifth postulate from his [Proclus] own axiom.
I think that all ancient attempts (at least up to Saccheri) to prove Euclid Fifth postlate was grounded on the belief that it is (obviously true but) not "evident"; thus, it must be proved on more evident principles.
Only after Saccheri, Lambert and modern non-euclidean geometry the independence of Euclid Fifth postulate was understood.
Thus, prior to this understanding, the idea of its equivalence with other principle was , if not meaningless, quite "uninteresting".