I'd use 'greedier'. But it's a very sweeping statement.
I know it is not the best way to start a sentence with "but" but there was a comma splice. Are my corrections correct?
Although it is out of my league to correct your mistake (please do not mind Rover sir) but I just gave it a shot. There is a saying "nobody is perfect" so teachers are human being as well they can sometimes make mistakes.
Congratulations! You spotted and corrected the missing apostrophe. You should have stopped there. While dividing a perfectly good sentence into two was unnecessary, your sentences are okay. But you should think carefully before you begin a sentence with a conjunction.