Both of you are correct! Certainly the basic reason for the mitzvah of giving charity is to help the needy, as you thought. But the mitzvah is also for the benefit of the giver. What does this mean?
Sometimes I hear a person say after giving charity or helping another person in some way, “Ah, I feel so good about what I did to help someone else. And thank God that I am well-off enough to be on the giving end, and that I’m not poor or needy like the person I helped!”
This good feeling is certainly a benefit to the giver of charity, but Judaism teaches that the giver’s benefit is so much greater and significant than this relatively superficial benefit of feeling good.
In the Talmud (Bava Batra 10a) we find a fascinating dialogue on the reason for giving charity. The Roman ruler Turnus Rufus asked Rabbi Akiva, “If your God loves the poor, why doesn’t He support them?” Rabbi Akiva replied, “So that we may be saved by them from the judgment of gehinom (i.e. a harsh judgment in the Afterlife.” We learn from this that an important reason for giving charity is to provide opportunity to gain great merit and reward in the World-to-Come by giving charity to the needy. One way to look at this is that not only does the giver do a mitzvah by giving, but the needy recipient also does a mitzvah by providing the giver with an opportunity to give. I’m certain that this is what your friend meant by saying that giving charity benefits the giver.
And besides giving charity protecting the giver from a harsh judgment from Above as we are taught “Charity saves from death” (Shabbat 156b), let’s also remember what Rabbi Yehuda taught us, “Great is charity, for it hastens the final Redemption” — i.e. world peace and universal knowledge of God. (Bava Batra 10a)
