There are a number of ways you can increase you proficiency and confidence in crosswinds. I used one or a number of the following:
1. Schedule a crosswind circuits lesson with an instructor. In a C-172 I would recommend something between 15-20 kts crosswind. It would only have to be around 45mins long and you can get 6-7 circuits in.
2. During your CPL VFR navigation 'hour building' dual flights you can practice at one of the airfields you go to if there is a sufficient crosswind available at the time.
The objective is to be able to quantify your crosswind limit. This way you and your instructor will know what you are capable of because you have actually done it.
As to your CFI, I agree with his "statement", however I reckon he's misplaced using that in this context when talking about 6-7 kts crosswinds. I would be encouraging you to increase your crosswind ability by doing a dual lesson.