Can hate to same gender parent cause homosexualism?
Gender is not, despite what others might say, a social construct, and neither is sexuality, just google David Rimmer to see what happens when researchers have messed with these. While we don't understand what causes homo-sexuality fully, typically speaking sexuality seems to be influenced by hormone exposure in the womb, when a human is a foetus. Although studies have found that roughly 5-10% of people have had same-sex sexual experiences, this appears to be relatively common in adolescence although it does happen later in life too. Speculatively its possible that this partly comes from people learning about themselves and their sexuality. However despite people having these same-sex experiences only 1-3% of people identify as homo or bisexual. Why do people have these experiences? There are a a multitude of reasons, some people are homosexual, while some may be curious or undecided, or perhaps some other reason. 

Ignoring the sexuality side and looking at group identification: people have all sorts of reasons for identifying with particular groups or demographics. While relationships with parents are certainly cause for being rebelliousness, its not going to turn anyone homosexual who isn't already inclined. There seems to be no recent evidence about parenting style and sexuality, apart from on religious websites that have no place here, although stonewall say that there is no relationship. However the research linking the two is absent, which usually suggests either it hasn't been researcher properly or, more likely, that there is no relationship at all.