How can a Christian reject part of the Bible and still call themselves a Christian?

[vorlon13]

I had a conversation with Christian girl yesterday and it randomly led to the subject of homosexuality.
She believes that it is perfectly acceptable to be a homosexual because you should be able to love anyone you want.
I asked her how she could say that and call herself a Christian. She became iritated. I pointed out that her Bible clearly states that it is an abomination. She finally said " I don't care what it says" and ended the conversation. The stress caused by the cognitive dissonance was pretty high.
I find Christians do this a lot. They reject what they don't like in the Bible.

You can't be a Christian unless you cherry-pick which parts you want to believe.  The bible is shot thru with contradictions.  If you read that god can do everything, and also that he can't defeat iron chariots, then you have to pick one or the other.  You can't believe both.

Atheists, on the other hand, can read the bible literally.  We can say, "That's a contradiction.  The bible has to be wrong about at least one of the two conflicting statements."

As an atheist, however, I can insist the christers witnessing the Word to me be of the stripe that do believe all the bible, contradictions and all.

That it is literally impossible is not my problem, it is theirs.