Why do some words take "ir" and others "un?" Is it mere euphony?

As in -- "Unlike the regular army, the irregulars are unreliable, unrealistic, and irremediable."

Unrecognizable, but irresponsible...
Unregulated, but irredeemable...

The prefix ir- is a form of the prefix in- 'not' that occurs before roots beginning with r. It appears in words borrowed from Latin. It is related to the English prefix un- 'not' and Greek a- 'not'. I'd say that words like irregular came into English by borrowing, but words like unrealistic were coined in English from the Latin origin word real and the native negative prefix un-. For example, the linguistic term irrealis was either borrowed whole from Latin or was coined by a person who knew Latin morphology. Also, cf. irreflective, unreflective, and non-reflective.

Another thing. There are two different prefixes in Latin with the same form, in- (and its various combining forms), one negative, meaning 'not', and the other intensifying, meaning more of the same. You can see these in various loanwords from Latin: for the former, irregular and illogical, but for the latter, incandescent and inflammable.