In addition to the answers that have already been given (which correctly point out that <PERSON> didn't actually himself summon the would-be council members to Rivendell,) it's important to remember that <PERSON> was still under the spell of <PERSON> at that time.
Since <PERSON> was under <PERSON>'s control, he'd almost certainly not have supported destroying the ring.
Additionally, as <PERSON> answer mentions, <PERSON> told the council,
What shall we do with the Ring, the least of rings, the trifle that <PERSON> fancies? That is the doom that we must deem.
That is the purpose for which you have been called hither. Called I say, though I have not called you to me, strangers from distant lands. You have come and are here met, in this very nick of time, by chance as it may seem. Yet it is not so. 381
Believe rather that it is so ordered that we who sit here, and none others, must now find counsel for the peril of the world.
Presumably, at least by <PERSON>'s belief, whoever or whatever 'ordered' things such that the members of the council would be in Rivendell at the right time would have been aware of <PERSON>'s control over Théoden and, thus, did not want a representative of Théoden to be present in order to prevent news of the council's intent from reaching <PERSON> (and, from <PERSON>, likely also <PERSON>.) Keeping <PERSON> from knowing their plans to destroy the ring was key to being able to ultimately carry out those plans. <PERSON> spoke of the desire to maintain this secrecy:
Let folly be our cloak, a veil before the eyes of the Enemy! For he is very wise, and weighs all things to a nicety in the scales of his malice. But the only measure that he knows is desire, desire for power; and so he judges all hearts. Into his heart the thought will not enter that any will refuse it, that having the Ring we may seek to destroy it. If we seek this, we shall put him out of reckoning.
Thus, not having a representative of Théoden present was important to the council accomplishing its purpose. 381