However, cutting a hole in the front door (well, a bigger hole in this case; I already had a blocked-up cat door there from very long ago) is a serious commitment. It affects both the security and weatherproofing of your house. Standard commercial dog doors are a) expensive and b) while they are reasonable at keeping the cold out on still days, they leak around the edges in a stiff wind, which we get a lot of here. I'd seen a two-flap design years ago, and even made a small one that worked okay out of car floor mats, so I decided to scale that up, using a cheap vinyl set of mats from Big Lots.
Long story short, I found that even when reinforced, the mats didn't hold up very long, though they got me and my dog through that weekend trip. However, I had already cut the big hole in the door, so it seemed a shame not to build something that would work over the long term. I slapped a piece of plywood over the opening to keep the weather out and went back to the drawing board.
First of all, the theory. A dog door that overlaps the main (human) door around its edges when closed is inherently more weather-resistant than one that just fills the opening. Only problem is that—unless you have a very clever and agile dog—this only works one way. With the two-flap solution there are in fact two dog doors: (1) the larger one which overlaps the outer surface of your main door, and which can be pushed open from the inside, and (2) a slightly smaller one that fits inside the other and can be pushed open from the outside. Both have magnetic catches that keep them in place when not in use.