The question came up again: Don’t we have to remove all the paint before painting again? Well not always, as a general rule, you are time & money ahead if you cover over old coatings rather than remove them with few exceptions for us house painters. One exception is if you wanted to remove all the lead based paint from your property; that is call abatement. Usually a good scraping, sanding and cleaning will create a solid surface to prime and paint.
Yet there are those times when coating removal is necessary. When old finishes are deeply cracked, blistered or peeling it takes a careful hand to scrape and sand, so complete removal maybe in order. Chemical stripping is a slower process than mechanical methods (palm sanders, etc.) but maybe needed with complex ornate work. Much has to do with the time, money and risk you are willing to undertake when repainting.
Simply covering the old stubborn coating is an easier job. Of course, a decision must be made as to what is an acceptable appearance is when finished. If you don’t mind the plateaus here and there under your paint from stubborn previous coatings or if it would look better entirely smooth? The choice in primer and paint can accentuate the visible results between stripe or cover. Note: higher glosses tend to emphasis the imperfections in the surface preparation. A myriad of circumstances and conditions need to be considered before that paint brush is picked up.