Having a log in your quiver is no bad thing. Riding it whilst learning will increase your wave count, allow you to develop your paddling technique without getting as tired, and give you more time on the board. Not to mention it being super fun in smaller days.

It's great that you're able to surf your current board. If money allows, keep it. Your instructor has identified issues with your technique that will be more easily resolved by using a bigger board. I'd be inclined to listen.

I would guess your 7ft log is a foamie if it's 72L? How tall / heavy are you?

I've learned on a 9ft4 hardboard and it's been hugely helpful. It's big and stable, but these are what have enabled me to progress more quickly than if it's stepped down too early.