Need to ask this question cause I am confused. My daughter is 3 years old and I am her father, my wife has voiced concern about the following situation.
At bedtime I take her to bed and lay down next to her on top of the covers fully clothed and tell her a bedtime story. She and I both enjoy this.
For me this is totally natural for a father wanting to do this. My wife however, says that it is inappropriate for me to lay next to her and instead I should sit on the bed. When I ask her to explain to me why she thinks it inappropriate it is because in her culture (catholic) little girls should be little girls and this type of behaviour of a grown man laying next to a young girl is wrong.
Unless something is happening, which it is not I do not see any thing negative to come of this behaviour for her. When she tells me to stop or she gets to a age that I think it is inappropriate then I will stop.

What do people think? Am I being unreasonable or does my wife have a point?

I honestly do not think there is anything wrong with the way you read a book to your daughter. I don't know why your wife would have 'inappropriate thoughts' regarding this unless there is something in her background to make her think about it,

I know you want to prove a point, and rightly so, but maybe you should honour her request that you sit on the bed instead. It just is not worth creating a problem involving your child.

I agree that there is nothing wrong with this. Our modern society is far too afraid of touching children when touching per se isn't the problem. A child (boy or girl) who snuggles next to either parent to be read to will have a much healthier life and relationships. You could suggest that she talk to her priest, and I'll bet he will tell her it's fine.

But I also agree that compromising with your wife is a good idea. Maybe an armchair in your daughter's room, or on the living room couch. It's the contact that is important, not where it is.

This is not a catholic thing, your wife has issues that need to be addressed.
Was she molested as a child ?

Catholic parents will lay with the child in bed all the time. I have no idea what she is talking about

I used to do that for my daughter all the time... I had no bad intentions and I'm sure you don't. Sometimes I even just stayed there until she fell asleep. I see nothing wrong with it as long as you know when it is time to stop doing this.

Your wife has issues that should be explored. Please let her read this thread. There is nothing wrong with what you are doing. I used to cuddle with my daughter way past 3 years old.

Her fears have nothing to do with Catholicism. There is some other issue causing her to react this way.

What you are doing is what any GOOD father would do in that you are comforting a 3 year old at bedtime which can be a stressful time in the day of a toddler.

You appear to be a very caring father. Keep it up!

Just a side note but Roman Catholic is a religion, not a culture. I'm not sure OP isn't mixing up cultures and religion.

What cultures and religions are involved here?