How do I say this in a more professional way?

[BananasAreEvil]

I fully appreciate where you're coming from

It’s difficult to advise without exact circumstances, however if your manager is making a decision that is legally appropriate you must give compelling business reasons why your solution is better.

Perhaps something on the following lines:

I appreciate that the law doesn’t entitle me to work a 4 day week however because I can focus on X/not getting distracted by Y/study on my day off this will lead to better increased revenue/better client engagement/improved business outcomes.

Your starting point is to list WHY it is better for you to work 4 days. There can’t be many circumstances where a shorter working week would be beneficial from a business perspective do making that really clear is critical to your negotiation.