I am complete within myself, I don't see the need for another person to "try" and complete me. Be happy with who I am and compliment that, accordingly I will compliment her as well.

Well lets get technical here Peccy. Didnt you know?

"The Collaborative International Dictionary of English v.0.48"
Compliment Com"pli*ment, v. t.
To praise, flatter, or gratify, by expressions of
approbation, respect, or congratulation; to make or pay a
compliment to.
1913 Webster


"The Collaborative International Dictionary of English v.0.48"
Complement Com"ple*ment, n. L. complementun: cf. F.
compl'ement. See Complete, v. t., and cf. Compliment.
1. That which fills up or completes; the quantity or number
required to fill a thing or make it complete.
1913 Webster

2. That which is required to supply a deficiency, or to
complete a symmetrical whole.
1913 Webster

History is the complement of poetry. --Sir J.
Stephen.
1913 Webster



Bad choice of words?

No it would be rhetorical if to complement and to complete meant the same thing.