Standard young-Earther responses, taken from when I was a young-Earth creationist.
Round Earth: Yes. You sort of have to stretch to interpret the Bible as saying the Earth is round or flat, so it’s not exactly a contradiction. Things like “the four corners of the Earth” are obvious metaphor.
Animals on the boat: The “kinds” of animals (Hebrew “baramin”) don’t correspond exactly to what we call species. There are fewer animals in the ark than 2*(number of modern species); this is considered to be a sufficient answer even though it probably isn’t. I don’t know exactly what level of generality the baramin are supposed to be; I guess it depends on how much evolution the particular creationist is willing to accept. They’ll typically use the example of dogs and wolves being the same “kind,” but if that’s the level of similarity we’re talking about then there’ll still be an awful lot of kinds.
Amount of water: The Earth used to be a lot smoother. Shallower oceans, lower mountains, etc. So it could be covered with a more reasonable amount of water. We know this because in the genealogies some guy named his son after the fact that “in his day the Earth was divided.” (The word for divided, Peleg, means earthquake or cataclysm or something. This verse also doubles as tectonic plates being moved around.)
I don’t agree with these, but thought that to avoid strawmanning I should post the l responses that I would have used. Not that they’re much better than the straw version, but this is the kind of thing that would have been said by at least one YEC.
I once believed that six times one is one.
I don’t remember how it came up in conversation, but for whatever reason numbers became relevant and I clearly and directly stated my false belief. It was late, we were driving back from a long hard chess tournament, and I evidently wasn’t thinking clearly. I said the words “because of course six times one is one.” Everyone thought for a second and someone said “no it’s not.” Predictable reactions occurred from there.
The reason I like the anecdote is because I reacted exactly the same way I would today if someone corrected me when I said that six times one is six. I thought the person who corrected me must be joking; he knows math and couldn’t possibly be wrong about something that obvious. A second person said that he’s definitely not joking. I thought back to the sequences, specifically the thing about evidence to convince me I’m wrong about basic arithmetic. I ran through some math terminology in my head: of course six times one is one; any number times one is one. That’s what a multiplicative identity means. In my head, it was absolutely clear that 6x1=1, this is required for what I know of math to fit together, and anything else is completely logically impossible.
It probably took a good fifteen seconds from me being called out on it before I got appropriately embarrassed.
This anecdote is now my favorite example of the important lesson that from the inside, being wrong feels exactly like being right.