I've never heard of a coach "pressing" a team. Pushing, yes. Pressing, no.
"Press for an Answer – to insist someone answers a question Historically, torture victims used to have more and more weights placed on their chests until they confessed, making them literally 'pressed for an answer'."
This is an example where English has got weird in my lifetime. "Press" is old fashioned. When I was young you would have described a coach as having "pressed" his team. As I was in my teens the word became "pressured", but that didn't last long. Eventually it became "pressurised". It seems to be just adding syllables for the sake of it. I wonder what syllable could be added to it next?
Same here (not a native speaker, though). Pushing seems to make more sense.