repel vs push back

repel is not a noun while push back is a noun.

Word	Noun	Adjective	Verb	Adverb
repel	No	No	Yes	No
push back	Yes	No	Yes	No

As verbs, repel and push back are synonyms defined as:

Other synonyms of repel include beat back, drive, force back, repulse.

repel (noun)	push back (noun)
	the act of forcing the enemy to withdraw

repel (verb)	push back (verb)
reject outright and bluntly	cause to move back by force or influence
force or drive back
cause to move back by force or influence
be repellent to; cause aversion in
fill with distaste