How did your parents react to you coming out of the closet for your sexuality?

I haven't actually told my parents that I prefer women yet. One time I tried to explain that I was asexual (I identify as a Grey-A) to my mom and her response was basically "Oh that's normal! I don't really like sex, either, but it's an inevitability of life." and that was.........really alarming....................................
I don't think my parents would disown me or anything for being a lesbian, I just don't see a point in telling them this kind of stuff until I'm in a serious, committed relationship or something.

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