[Maédhros]

`He is debating which course is the most desperate, I think,' said Aragorn. 'And well he may. It is now more hopeless than ever for the Company to go east, since we have been tracked by Gollum, and must fear that the secret of our journey is already betrayed. But Minas Tirith is no nearer to the Fire and the destruction of the Burden.

`And so should I,' said Gimli. 'We, of course, were only sent to help the Bearer along the road, to go no further than we wished; and none of us is under any oath or command to seek Mount Doom. Hard was my parting from Lothlórien. Yet I have come so far, and I say this: now we have reached the last choice, it is clear to me that I cannot leave Frodo. I would choose Minas Tirith, but if he does not, then I follow him.'

'It would indeed be a betrayal, if we all left him,' said Aragorn. 'But if he goes east, then all need not go with him; nor do I think that all should. That venture is desperate: as much so for eight as for three or two, or one alone. If you would let me choose, then I should appoint three companions: Sam, who could not bear it otherwise; and Gimli; and myself. Boromir will return to his own city, where his father and his people need him; and with him the others should go, or at least Meriadoc and Peregrin, if Legolas is not willing to leave us.'

Based on the facts that Aragorn had at that moment, I think that he made a wrong and "illogical" decision. I think that if had spilt up the company say: Legolas and Gimli following the Orcs and M & P, and he himself to go after Sam and Frodo.
Aragorn knew that Gollum was following them. He knew that Gollum was "evil" and that he would hinder or even attack Frodo.
He abandoned the Quest to try and rescue two of his companions.
It doesn't make sense to me.