You are 100% wrong. They are insults because of sexism/homophobia. You honestly think it's just random that words that are associated with victimised minorities are also those used as casual insults?
The correlation only exists in your mind and the minds of other lesbians.
If someone calls someone a pussy, they mean he is a coward. They do not mean he is a literal vagina or go through a lengthy thought process of the etymology of that particular word and its relation to homosexual men.
I know it doesnt particularly make it right but, in this instance, calling someone a pussy and a cunt is pretty far from casual sexism in its intent. The fact that you have made such a big deal about it has just drawn attention to the connotations you are objecting to.