Especially for teenagers/young adults, it is better to avoid close friendships with people of the opposite gender whom you cannot marry. At this age, feelings develop easily, and it can lead to wrong actions or heartbreak (or both). There are also a lot of hormones that interfere with good judgment. Sometimes, being forbidden from being with someone makes you want them more and that can lead to a Romeo and Juliet type of situation which doesn't work out well for anyone.
Also, it may lead to false hopes, e.g. fantasizing that he might convert to Islam, whereas that is unlikely. I think in general, girls tend to look at young men as potential life partners at a younger age than guys. So it is likely she might end up emotionally dependent and starting to build up the illusion that they will be together in life, whereas this is unlikely to happen in real life. At the same time, his mind might be entirely on pursuing his own goals in life and not sharing this idea.
Islamically speaking, it isn't appropriate to be spending time alone together, going places together, being emotionally intimate with each other, touching each other in any manner, etc.
I am not saying there is no possible benefit to the friendship as friends can help us through all sorts of life challenges, but just that it's better to be cautious and more distant.
The way to do that is just being less close and communicating less and etc. Friendships also take their own course and people often move apart in life, especially after graduation.