Council tax income goes to the council who use it towards providing local services with additional income coming from Central Govt from our IncomeTax.
Much of this money pays for services we all use such as education, fire service and police service, refuse collection, tree surgery, parks and recreation services, libraries, looking after roads, pavements and cemeteries etc.
These services aren't just used by property owners, they are used by everyone who lives in those properties.
It isn't a tax on home ownership. A landlord doesn't consume any more of those services than anyone else. Why shouldn't a tenant pay towards the services that they benefit from?
What about council houses? Do you think tenants shouldn't pay so the Landlord (the Council) has to pay itself?
We all have a responsibility to collectively pay for the services consumed locally. Some people don't have kids yet they pay full Council Tax forever, long after their education has been repaid. By your reckoning a tenant wouldn't contribute yet would use all the services a council provides for free.
An afterthought
Have you raised this because of the idea from the Labour party a couple of weeks ago that tenants shouldn't pay Council tax?