For dialogue, it is logical for the Catalyst to argue for Synthesis. In its own words "it's the ideal solution". It allows to execute the very solution it's trying to achieve from the start - merge organic and synthetic life. In its mind it is the most logical and perfect solution.
That, I get and it's fine (as far as the catalyst's motives are concerned)
Control and Destroy result in it being changed/destroyed and it actively tries to oppose it.
No it doesn't. It is passive, not active. Shepard is the one who makes the decision and the catalyst presents them. If it were active, it would prevent Shepard from choosing the other two, which - as we previously established - it could.
For as long as you haven't picked a choice, the old solution is still working - harvest continues. It does claim that the solution will not work anymore, but that is applied to the next cycles.
I think we are going in circles here. This is somewhat contrary to the idea in your previous post, that the catalyst is realizing that it and it's reapers are part of the problem. Remember, the catalyst came up with the harvest and reaper idea itself. There is no shackle on it that makes it harvest.
It is also tied to the second problem you mentioned. It can't just stop, doing so will mean abandoning the solution of the problem, its task. Destroy doesn't solve it either, but there will be no Reapers around to interfere, it's still a chance for the organic life to develop a new solution.
So what distinguishes destroy from the catalyst just stopping on his own?
Organics have the understanding of Reaper technology (and perhaps even more from working on the Crucible). And no cycle had proven more capable than this one. Reapers are a great example of what the synthetic life can achieve and they had countless cycles to evolve. If organics can destroy the Reapers, they will be more than ready for any new emergence of hostile synthetic life.
But they can't destroy the reapers. They can only destroy them because they let themselves be destroyed. The catalyst even says that it believes so himself "your children will create synthetics and the conflict will begin again."
However, it 1) doesn't leave Catalyst an option to monitor the situation (and is perhaps viewed as abandoning its task)
So it does abandon it's task after all with destroy? (see my other question above)
2) will result in a loss of synthetic life (now and in the future, peace won't last) and so it advises against it.
Ok, so if I understand this correctly, you are saying that it's ok for the catalyst to stop the cycle now if Shepard chooses destroy because after that, the organics have the crucible and therefore destroy any future synthetic life all over again as often as they like. Therefore it is ensured that organics will always be "on top" so to speak. Please correct me if I am wrong, 'cause I am really not sure if I interpret you correctly there.
Problem is: the crucible requires the catalyst to work. We actually have no idea how it works (as Shepard even tells the catalyst), why it needs the catalyst or how it destroys the synthetics. All we do is shoot a tube. The catalyst (i.e. the synthetic) actually works the magic. So now we can build a super-weapon against synthetics that can only be operated with the help of synthetics.
We could continue extrapolating scenarios here but I guess the crux is, that destroy doesn't change the galaxy a lot. It doesn't suddenly give us some new tech, we couldn't have anyway and it doesn't give us some greater understanding and it doesn't protect us from the synthetics in the future (as the catalyst states itself). The only thing it does is that the catalyst and the reapers basically commit suicide with Shepard's help. So I still don't see the motive for it to offer the choice.
{Sorry for taking your post apart. I usually hate doing it but there were a lot of different notions in this post and addressing them in just one answer was a bit too much of a wall of text.)