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Sounds like your husband needs some good male influences. Some friends who either don't have working wives, or who do but complain about the fact.

OP here.
Of course.

2. He wants two incomes because he likes a good life style.

The best way to argue against this is to sell him on the idea that if you stay at home with the children, you can "add value".  Not in monetary terms but in terms of getting chores done that would normally have to be done on the weekends.  For example, what are some things that you both have to do on the weekends because you can't do them during the week while you work?  Laundry?  Grocery shopping?  Cleaning bathrooms?  If you can convince him that you can do these things while staying at home, then you can persuade him that the weekends will have "more free time and less chores" if you stay at home.  Then weekends will be better for him and everyone.
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Also, go to your friends who pay for child care and get quotes on what they pay.  Compare that to how much your "take home" pay is from work.  I've heard many people complain that most of their work $ is spent on child care so having a job isn't a great benefit.  It's almost a wash.

8. ... He will never agree about this and he will go on talking about how mothers who stay at home dont develop themselves.

Next time this conversation comes up, remind him that the purpose of marriage is for the education and development of their children.  The woman's job is not to develop HERSELF but to develop/raise the children.  Yet, she will develop all kinds of skills by helping her children.  A wife has to learn the following.  A mother was not called a "domestic engineer" for nothing:
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1.  Nursing skills and basic medical knowledge for all kids' needs.  2.  Accounting/budgeting when buying clothes/food.  3.  You can take some cooking/baking classes to better learn how to cook great/thrifty meals.  4.  You could learn sewing so you can make children's clothes or mend them.  5.  You'll have to learn/re-learn science, math and english too so you can help your children in their school studies.  6.  You'll (possibly) have to read psychology/personality books to learn how to deal with a difficult child or situation.  7.  You'll be able to run errands during the day that typically can only be done on the weekends (or at night after work), if both work during the day (dry cleaning, groceries, car maint, laundry, house cleaning, etc).
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There's lot of advantages to having a spouse stay at home.  There's plenty to do and plenty to learn.  And a lot of economic benefits too.

Lot of good advice in this thread, and good insights.
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Let me look at the problem from a broader, general view.  The problem isn't that your husband wants you to work so much as it is that your husband is very worldly.  What are the various influences around you two that could help improve that problem?  Are you friends with other Catholic couples?  Can you naturally and authentically put your husband in touch with masculine men who don't make their wives work, who are disdainful of popular culture, and so on? 
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Your husband may be Catholic but he seems to all but entirely lack a Catholic moral and social sense.  Even if he was OK with you staying home with the kids, something else would rear its head.  This is just the way the problem has happened to manifest.  What about when your daughters are sixteen and he's OK with them dressing like sluts, or what about when your son is eleven and you don't want to give him a smartphone because of risks to impurity but your hubsand thinks looking at porn is "natural"?  What I'm saying is that while it's obviously important to try to find a way to get him to let you stay home, if he "gives in" on that but remains worldly you're not actually solving any underlying issues.  In fact without solving underlying issues he's probably going to resent you for staying home.