Why did Catalyst offer the other options to Shepard at all?

Question

In Mass Effect 3,

Catalyst is the Intelligence created by the Leviathans to maintain peace between organics & synthetics. When that proved impossible, Catalyst chose to create the Reapers and start the cycles to prevent the inevitable conflict while preserving all advanced organic and synthetic life.

Shepard's arrival is evidence that the solution no longer works. A new solution is needed, and Catalyst knows that Crucible offers new options that Catalyst cannot achieve alone, but with Shepard's help it can. The three options are to Destroy, Control or Synthesis. Catalyst offers all three options to Shepard, yet at the same time, it already knows that Synthesis is the ideal solution: it is the final evolution of all life, organic and synthetic, and all of Catalyst's original objectives of preserving life and preventing organic-synthetic conflict can be achieved without the need of the cycles anymore.

The above is with reference to the below video major ending spoilers:

If Catalyst already believes that to be the ideal solution, why offer the others to Shepard at all and risk him not choosing the one Catalyst believes will achieve all of its objectives?

Looking for in-universe reasons not based on game mechanics, so "Catalyst needed him to have more War Assets to choose that" doesn't make sense in-universe.

Answer 1

Looking for in-universe reasons not based on game mechanics, so "Catalyst needed him to have more War Assets to choose that" doesn't make sense in-universe.

This mechanic is justified in-universe by the argument that a weaker fleet during the end game will result in more damage to the Crucible, which will make it less capable of functioning to its fullest extent.

But you still get a choice even with maxed war assets, so this is not an adequate explanation by itself.

From the video you helpfully provided:

Catalyst: There is another solution: Synthesis.
Shepard: And that is?
C: Add your energy to the Crucible's. The chain reaction will combine all synthetic and organic life into a new framework. A new... DNA.

(At this point I had to find a video in which Shepard asks for more information.)

S: Explain how my energy can be added to the Crucible.
C: Your organic energy, the essence of who and what you are, will be broken down and then dispersed.
S: To do what, exactly?
C: The energy of the Crucible, released in this way, will alter the matrix of all organic life in the galaxy. Organics seek perfection through technology. Synthetics seek perfection through understanding. Organics will be perfected by integrating fully with synthetic technology. Synthetics, in turn, will finally have full understanding of organics. It is the ideal solution. Now that we know it is possible, it is inevitable we will reach synthesis.
S: Why couldn't you do it sooner?
C: We have tried... a similar solution in the past. But it has always failed.
S: Why?
C: Because the organics were not ready. It is not something that can be... forced. You are ready. And you may choose it.

From this we can see that the Catalyst is unwilling to force the synthesis ending, because forcing it has failed in previous cycles.

Commander Shepard is the leader of the resistance against the Reapers. The Catalyst believes the Commander is the only person qualified to make this decision on behalf of the galaxy, because no other cycle has ever gotten as far as Shepard's did, and that was entirely due to Shepard's competence and determination. In particular, the Catalyst does not consider itself qualified to make this decision, because it has chosen incorrectly in the past.