[Math] Why did the ancients hate the Parallel Postulate

Question

I am reading this book, Gödel's Proof, by James R. Newman, at location 117 (Kindle), it says,

For various reasons, this axiom, (through a point outside a given line only one parallel to the line can be drawn), did not appear "self-evident" to the ancients.

Any idea what the various reasons might be? It's self-evident enough to me.

Edit

Sorry, my bad, right after the sentence, (the above quote), there is a footnote, says that:

The chief reason for this alleged lack of self-evidence seems to have been the fact that the parallel axiom makes an assertion about infinitely remote regions of space. Euclid defines parallel lines as straight lines in a plane that, "being produced indefinitely in both directions," do not meet. Accordingly, to say that two lines are parallel is to make the claim that the two lines will not meet even "at infinity." But the ancients were familiar with lines that, though they do not intersect each other in any finite region of the plane, do meet "at infinity." Such lines are said to be "asymptotic." Thus, a hyperbola is asymptotic to its axes. It was therefore not intuitively evident to the ancient geometers that from a point outside a given straight line only one straight line can be drawn that will not meet the given line even at infinity.

Answer 1

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.