So outsized is Garfield's self-regard that he does not differentiate between the sort of feelings Jon has for his girlfriend and the feelings he has for his pet. Garfield may or may not be half-joking in his eyelash batting and the flirty pose he strikes, ignoring the gulf of aesthetic standards and nature of the relationships. But whether Garfield equates, conflates, confuses, ignores or blurs these separate concepts of beauty, he does so because he cannot conceive that they co-exist, that Jon could appreciate both kitty and woman in different ways. All Garfield sees is that someone else is occupying some of Jon's brainspace, usurping the center of attention, he is not being treated as special and perfect, and in his last line shifts his shame onto someone else.
Here is a case where Garfield's enormous vanity works at odds with his propensity to sloth and gluttony. Garfield does nothing whatsoever to "keep [himself] up," unless we mean that he rigorously maintains a body shape like several water balloons in a fur backpack. These contradictions run deep in Garfield, tentacles rising out of a bottomless pool of aggressive narcissism.
The third joke is that Jon's experience of this conversation is his cat making a weird face at him — possibly he even understands that the cat is flirting with him — which he thinks is "strange." And even if Garfield actually were expressing sexual feelings for his owner, the reality is far stranger than Jon knows, as Garfield seems to be using the Hare Psychopathy Checklist as a lifestyle guide and has gotten halfway through.