
Not promoting does not equal hating. The Catholic church makes it a point to accept all, and while they will not support same-sex acts, that does not deny one from taking part in the church. The sacrament of marriage is specific to man and woman as two parts of one whole, it is a religious ceremony, not the legal version, so of course they would not recognize same-sex marriage as the same as the way the church does marriage.
Sure in theory, but also it is more complex than that label. I am a bisexual catholic. I feel the desire to have both heterosexual and homosexual relations, and while I may falter or sin, I also understand that it is a sin. I do not hate that side of me nor do I suppress it, but I know that it is not what I wish to prevail.
You can view it like that but the main belief is that those feelings and identities are real but also misdirected. Urges are not mental illness or sinful, but we are called not to act upon them. You need to understand that the catholic view is that sex is the ultimate bonding of two people in creating new life, marriage is the bonding of two halves into one while they live, identity is bound to soul and spirit as much as body and mind. There are foundational conflicts that make it uncomfortable.
A sin is a divergence from God, or a divergence from the order of the world. It is not that they are evil, but they are unintended or misguided steps away from the path laid before us. The reason why it is so important is because those diversions literally take one farther from God, still loved the same, but they separate the person from one-ness with God.