Welded wire is a lot less expensive than hardware cloth so if you have to come to a compromise that is likely a good one. It also doesn't rust and will last a long time unlike chicken wire (which should be a good selling point for your dad).
Since he bought that nice frame it only makes sense...
Facts and logic can sound like "I am right and you are WRONG" which is never a good strategy to take with stubborn men. Plus he may not want to use hardware cloth because it is quite a bit more expensive.
If logic doesn't work try playing on his emotion by saying something like "It may be...