Renting a church kitchen seems like a no brainer for a caterer, to the point that it's almost surprising that all churches and caterers aren't involved in symbiotic relationships. Since the world isn't arranged that way, you've got to figure there are [gasp] reasons.
In most localities the practice is prohibited by relevant health departments, which is not a good thing for you. And, there are often problems for the church with the IRS and/or insurance as well. These complications may partly explain why you can't find a willing church.
"Usually" and "can be" don't necessarily apply to your location and situation. If you find a willing church, check with the relevant health department(s) -- city, county and state -- and see what kind of answers you get.
In the meantime, you may want to call other local caterers to (a) see what they do; and (b) inquire about sharing their space.
There are all sorts of contingencies which might make building a license-able kitchen on your land make sense. However, usually, assuming you have reasonable expectations of an ongoing, profitable business, it makes better financial sense to start with a lease. It's a nice write-off, easy to figure; and if you change your mind you're not stuck with a facility. If you don't already have an accountant who can advise you about this you're probably not at the point where building your own kitchen makes any sort of sense at all.