The appropriate size of an emergency fund depends on your insurances. If you can't cover an insurnace deductible in an emergency, then you don't have enough savings. If your deductible is low, then you are wasting money paying the insurance company a ton of money each month.
The sweet spot tends to be about a $2000 deductible for health insurance, homeowners insurance, etc. That $2000 also happens to match what it would cost to get a running car if yours is wrecked, to replace an engine or transmission if it breaks, to replace a broken furnace, etc. So, I like to tell people to get $2000 in an emergency account. If your emergency is bigger than that, then you have a big lack of insurnace policies that should be corrected. No emergency should cost much more.
Of course, that is just a starting point. You can have more than $2000. But the majority of people will never even reach $2000, it is silly to recommend more than they will ever have. Plus, once you go much over $2000 you just have money earning next to nothing when you could be paying off much bigger loans.
Once you get $2000, get yourself a safety net. Build up some leeway so you can borrow money if you really need it. That means paying off debt and eventually building wealth. I'd rather have $10,000 in investments earning 8% interest and get a $10,000 loan against it if a rare situation comes up than have $10,000 sitting idle at 1% or less in a bank just in case something that probably will never happen actually happens.