While I broadly agree with this, I would say that my own attempts at making mint sauce were fairly disappointing in comparison with shop-bought - Colman's mint sauce is an awful lot nicer than anything I was able to make, and (though I've never tried to make it) I bet their wonderful mustard is too.
You will probably also not be able to make at home anything all that similar to the mayonnaise you buy in a shop, though what you can make at home will almost certainly be equally as nice (my children were confused by the yellowish colour of home-made mayonnaise, which is sort of backwards since the confusing thing ought to be why shop-bought mayonnaise is white!).
Another advantage is that making your own x from scratch is fun and satisfying. Mayonnaise, mustard, soda, barbecue sauce, gravlax, liver sausage — it's fun to see the things people buy ready-made, and know you have the knowledge and ability to do it yourself. Sometimes it's enough better to be worth the effort; sometimes, like catsup, you find that the store-bought is better — but you still have the fun of doing it and the satisfaction of knowing for sure.
You will probably also not be able to make at home anything all that similar to the mayonnaise you buy in a shop, though what you can make at home will almost certainly be equally as nice (my children were confused by the yellowish colour of home-made mayonnaise, which is sort of backwards since the confusing thing ought to be why shop-bought mayonnaise is white!).