Because they were headed that way anyways

The answer is in the line immediately following the one you had bolded.

Legolas shall be for the Elves; and Gimli son of Glóin for the Dwarves. They are willing to go at least to the passes of the Mountains, and maybe beyond.

It was never the plan for the fellowship to accompany Frodo the whole way. Many of them had different destinations in mind (Aragorn and Boromir were headed to Gondor, Legolas to Mirkwood, and Gimli to Erebor.). But they would all at least need to cross the Misty Mountains together, and so set off in a group.

If you look a few lines past where you quoted, you'll see that Aragorn and Boromir are also explicitly said to only be in the group for convienceconvenience.

‘I would have begged you to come,’ said Frodo, ‘only I thought you were going to Minas Tirith with Boromir.’
‘I am,’ said Aragorn. ‘And the Sword-that-was-Broken shall be re-forged ere I set out to war. But your road and our road lie together for many hundreds of miles. Therefore Boromir will also be in the Company. He is a valiant man.’

And as Elrond reiterates right before they set off, everyone else was free to turn aside to their other paths as needed.

The others go with him as free companions, to help him on his way. You may tarry, or come back, or turn aside into other paths, as chance allows.