Your example piece is not absolute beginner material. It's hard for me to believe you really can't play basic chords like those and strike all the notes simultaneously. If you were asked to play a C
major chord in isolation (not as chord within a performance piece) are you really unable to strike all the notes simultanteously?
Unless your teacher is being super, super sensitive to the point of absurdity, I suspect you may in effect be playing an arpeggio during performance, like this...

...when the score doesn't actual have an arpeggio sign...

You may be doing this naturally. It does sound nice, more florid. But your teacher may be objecting, because it isn't in the score.
Also, I think rolling chords in this way can be a sort or performance strategy to work around accuracy issues. If you can't quite hit the whole chord with confidence and accuracy, you can get to the bass note first then role the rest of the chord. That buys you a bit of time to make the chord change. But the down side is it works around the accuracy issue ...and adds an embellishment not in the score.
I method I used to improve in this area was to play basic two chord changes repeated at octaves, like this...

You can use various chord changes like...

...and just move through the circle of fifths or transpose up/down chromatically.
Don't go faster than you can manage. Just do two octaves if that's easier. Visualize the keys you will be hitting in the new octave. Try actually looking at them before you put your hands on them. When you really visualize the target only then make the actual move. Do it quickly and confidently.
The strategy here works a bit backwards. As I said before, I expect you can play a simple chord. You don't need to practice that. You can do it, but you need to execute that at performance speed. In actual performance you need to strike chords without any delay. When your accuracy and confidence improves through the octave exercise you should be able to stop rolling chords during performance.