This is probably an example of spelling reform introducing ambiguity (cf. lé(igh)im), but the first-person singular of the present tense of léigh would be a synthetic form I.e. not followed by a pronoun (mé), in contrast to the past tense analytic forms, which do have pronouns, although synthetic forms are still to be found, mainly in Munster.
The irregular verb beir (rug in the past tense) actually means "bear", as in give birth to (bear children) or to carry.
The phrasal verb beir ar (rug ar in the past tense) is the Irish for "catch" (it's not the only way to say "catch" in Irish, but it's the one that Duolingo teaches).