My husband wants the unit on fan always to circulate the air is that not putting extra strain on my unit

No, assuming you are talking about the fan inside.
Running the fan constantly cost you electricity (money) but keeps the air circulating and at a more even temperature. That probably saves you money.

Running the fan constantly does not put an undue strain on the fan motor.

It puts strain on the fan motor and may shorten the life of it but I have seen units run like that for years with no adverse effect. It does, however, run up your electric bill. Many people use this practice with cathedral ceilings since it does do a better job mixing the air and cutting down on stratification.

I know this will be one of those 50/50 questions with answers. I Did a test with my heat pump system years ago. I used less electricity running the blower than with out. I ran it 24/7. But that's just me. I just now switched to a thermostat that checks to see if the equipment has ran in the last 15 min. if not it will run the blower for 15 min. Blowers are made to run. 6 years of run time my blower and it has never been changed.