Are geometric proofs less reliable than others?

When I submit a homework with a proof that uses a graph, ball, shape etc., most of the time the professors are not happy with them. They respond with a statement like:

"The proof you made seems very true but why don't you just make a usual proof without drawing anything?"

Of course this is something I can do, but I don't like proving something without any visualization.

So, is it because geometric proofs are more likely to be misleading?

Edit: For example: An open ball $B(x,\epsilon)$ is open.