Can you tell me what I'm doing wrong?

So I'm a college sophomore, and I have never had any dating experience at all. I never asked a girl out or anything to that extent. It's not because I didn't want to. It's just I could never get close to a girl to know if I wanted to or not.

Generally, what i do is initiate a conversation by talking about a assignment, the course, or something to that extent. 19 times out of 20 the conversation goes nowhere, because they are not interested. The 1 out of 20 usually ends up being a fairly lengthy conversation, but next class I can try to start a conversation with the same girl and nothing...
i've tried self help books on the subject of conversation and i try to do what it says but It's rather hard to continue starting conversations when i get so down after a failed one due to my depression and social anxiety. It's just frustrating.

I'm considerate, nice, polite, and intelligent, but from the looks of it I can't find a single person to make a acquaintances with, let alone find a woman who will start a relationship with me.

i just don't know what I'm doing wrong. I know my social anxiety and introverted personality are to my detriment, but I'm not overweight, hideous, or rude. So I'm just lost as to what my mistake is.

i've looked everywhere online for possible causes such as desparation, being boring, not being a active lister, arrogance, perverseness, but I just can't figure it out.

i know it's not coincidence or just miss fortune, because it has happened far to many times. And if it is just because I haven't found the right person, well than more than likely I never will.
Can you tell me what I'm doing wrong?
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