t I play at a Begginer-intermediate level....it can be until 10+ pushes....
I suggest, in your head, you redefine your level. If you cannot attack a push, to the extent that you end up in a pushing rally that goes on more than 1-2 pushes without you wanting to push, then you should consider yourself to be a straight, plain and simple, Beginner.
Then, you need to go through the process of learning how to loop those pushes, whether they are over the table or long. Someone above suggested getting a bucket of balls and to practice looping backspin over and over. That would be one way. I recommend you do some of that and some of the drill I describe below:
1) You serve backspin
2) Opponent pushes to FH side
3) You attack with FH
4) Play out the rally as though it was a point
&
1) You serve backspin
2) Opponent pushes to BH side
3) You attack with BH
4) Play out the rally as though it was a point
If you do that over and over and over, hundreds of times, you will learn to attack backspin. If you alternate, like you do 10 and then your opponent does 10, then you can both learn.
When you can attack backspin with both FH and BH, then the push in the drill can go anywhere.
When doing the drill, do not worry if your attacking shot lands on the table. You just have to keep trying to attack the pushes. Once you learn how, the ball will go on the table. Without trying, you won't learn. You just keep trying till you are topspinning the ball over the net and onto the other side.
When you can attack backspin with either wing, then you can consider yourself beginner/intermediate. Until you have that skill, you should not think of the word "intermediate" having anything to do with your level because that is an essential basic skill.