Go for it. I am a programmer (woman). Do very well. Started my own business doing development and have never looked back. Its a geat field, fast paced. always stuff to learn. You will never be out of a job, that is for sure. you say you are good with computers so I assume you have already started coding. So you already know you enjoy it and are good at it. Honestly, go for it. Its great!
Don't buy into the whole "women are not logical mindset". Its utter rubbish.
EDS - I just read the comment by the poster above me (incubus aka a bunch of symbols) and it made me very angry. So I am going to add that the beauty about computer science and programming in particular is that it IS logical. Which means it is really not that hard. You learn the language, u understand the syntax and you can make your stuff work. Sure your code might be messy at first and you might write more code than is strictly necessary, but as you get better you get more streamlined and efficient. Plus, you will find the community is very supportive of each other and freely share their knowledge in many instances.
Further, I have found that being a woman actually works to my advantage. Not to be sexist, but the stereotypical computer expert is often lacking in people skills and my clients value that I can pitch an idea and communicate it effectively in layman's terms.
Honestly, in terms of career choice, it is brilliant. there is so much scope. Don't let people like him put you off by pretending that you are automatically disadvantaged because you are a woman. Whatever flack you may get during your studies will all be forgotten when you enter the job market.