Why would an old two-prong 110V electrical outlet in an old house be wired with two hots instead of a hot and a neutral?

Depends upon what you mean by  "old two-prong" and "two hots".  Old house wiring didn't have color codes, so all the insulation was usually black. Did you actually measure the voltage across the two prongs?

In some old houses you can still find "crowsfeet" receptacles that allowed wiring for 125 or 250, as needed by a particular appliance. They were incredibly dangerous and were eventually banished from the electrical code.  This was about the time you still had "screw-in" receptacles that looked like a medium Edison light-bulb socket.

It wouldn't.

It Isnt. Check with a voltmeter. If both are hot, there is no potential between them.

You are seeing two black or two old fashioned  knob-and-tube bare wires. Don't let color fool you. Anyone can mistakenly tie blk to neutral. Electricity has no prejudice. 

Sometimes it is code to run a Red wire between switches like for upstairs-downstairs light control. 

Laziness. Somebody wasn't thinking.

If I had to guess I'd say someone converted the old dryer outlet to a 120v outlet, but got the wiring wrong.

This is how a former coworker destroyed my chop saw, running it on what he thought was a conventional outlet.

It wasn't. Someone didn't use what is currently standard color codes.

someone made and error. alternatively, someone rewired it to supply 220v even though doing so was improper and unsafe

If you get 240v between them then someone was being stupid and cheap not buying the right parts.

If you get near 0v between, but 120v on each to ground then you have a open (broken or switched) neutral. One is actually hot, the other is reading the same hot as open circuit voltage through some light or device plugged in somewhere else on the same circuit.

so that u can get 220 volts out of it if needed using the 2 hots and a ground wire

No but if I saw that I would assume that they set these outlets up in a series so they may have two grounds and two hots to complete the daisy chain. You may be looking at a neutral wire from a previous outlet in the series but your meter is saying it's hot because something else down the line is plugged in. A couple possibilities.

Only my two cents. Only a qualified electrician can say for certain.

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