I may be out of my league asking this, but I see this as a crucial matter.
"If Christ died for all, why did he predestinate only some to salvation?
The synergist will say it is because He knows who will believe and who will not.
It is critically important to understand monergists and synergists define "predestination" in two different ways. In monergism God assigned a destiny to each individual "from eternity," or prior to and without regard to events that transpired once creation was created. Synergists, on the other hand, define predestination categorically, not individually. In synergism predestination means that God has a destiny for unbelievers and a destiny for non-believers regardless of who those people might be. A non-believing person's destiny is hell unless and until he chooses to believe and that choice - the change from disbelieving God to believing God - that choice to believe is what moves him/her from the category of those (pre-)destined to hell over to the category of those (pre-)destined to eternal life.
Provisionist Leighton Flowers expresses it this way:
".....God foreknows in the sense that the elect one, who is Christ, he foreknows all those who would be in Christ by faith. In other words, they freely believe. In other words, it is their choice to believe or not believe, but God foreknows what will become of all who do believe, whether Jew or Gentile. And so, this concept of foreknowledge is a concept of God foreknowing and even pre-planning, in a sense what will come of whosoever is in Christ freely. In other words, they still have a free decision whether to be in Christ or not to be in Christ, but God has fore-ordained, or preplanned, based on His foreknowledge what will come of all who do believe in him freely." (time mark 6.35 in the video)
(I typed that as I was listening to it and didn't go back to check so I might have gotten a word or two out of order. Link and timestamp provided so everyone can hear him for themselves.)
It is worth noting Arminius would agree with the categorical definition of what Flowers calls "corporate" destiny but disagree with Flower's view of free belief. I point this out because the op specifies Arminianism, not any other synergism. This is kinda sorta important because 1) Arminianism is not as volitional as the other synergisms and 2) Christians often confuse or conflate all synergisms together as if they are synonymous when that is not true. Flowers is a radical volitionalist, a Pelagian, even though he vigorously argues against that appraisal.
The point is that Arms (and other synergists) define predestination differently. That means until the word is explicitly defined synergists and monergists are talking past each. They are debating a false equivalence. As long as the Calvinist is defining and defending monergistic predestination (God assigned the destiny of every individual without regard to the events within creation or the faculties or qualities of the individual) s/he has said absolutely nothing about Arminianism's predestination. The same works in reverse. As long as the Arm is speaking using an Arm view of predestination, s/he has said absolutely nothing about the monergistic viewpoint. It is only when the two groups, the monergists and the synergists, identify one of the two definitions as the specific subject of discussion that a cogent and coherent conversation can be had.
"If Christ died for all, why did he predestinate only some to salvation?
Do you mean the Arminian definition of "
predestinate," or the Calvinist definition of "
predestinate"?
If Christ died for all, why did he assign each individual a salvific destiny prior to their existence without regard to their character or the events of their life?
If Christ died for all, why did he assign them to a category of events that will happen to them after they have freely chosen to believe in him and become saved?
Those are two completely different and completely irreconcilable inquiries. So
which question is the op asking to be answered? 
The Arminian/synergist answer to the first question is, "
He did not such thing. That's a wrong definition of predestination so the question is a red herring." The Calvinist/monergist answer to the first question is, "
God has not answered that question other than to say it is because of His will and His purpose and not the will or works of the individual being saved and predestined to eternal life." Similarly, the Arminian/synergist answer to the second question is, "
Christ died for all but the benefits of his death are obtained by faith, so it is only those who freely believe in Jesus that obtain the destiny of all those who believe." The Calvinist/monergist will answer that question with, "
That is a wrong definition of predestination because people dead and enslaved by sin are not free to believe. The question is a red herring."
That being said, there is some common ground between Arminianism and Calvinism and some common ground between all synergisms and all monergisms. The common ground between classic Reformed Arminianism and Calvinism is that of total depravity. Arminius would have disagreed with Flowers and said no sinner is free to believe salvifically unless and until God has freed him or her to do so. Leighton rejects that position and says God made every human with the ability to believe and sin has not compromised or corrupted that faculty to the point of impotence. Monergism and synergism, likewise, agree the work of Christ's incarnation, death, and resurrection are
sufficient to save everyone but that work is effective or
efficient only in the lives of those who (salvifically) believe. Each group parts ways with the other over the matter of belief because in Flowersism belief is a freely existing faculty of the sinner and in monergism belief is proactively gifted to the sinner specifically for the purpose of effecting his or her salvation following his/her regeneration.
One last note: If anyone bothers to listen to the videos over at Soteriology 101 (or any of the other prominent sources for the various synergisms (
CCEL has the works of both Arminius and Wesley)
and pays attention to it you will find what I have recently said about synergist exegesis to be true: They invariably mishandle scripture in many ways. Chief among the mishandling is the practice of taking verses written
about the already saved and regenerate believer and acting as if they apply to the unsaved, unregenerate non-believer. Those two groups of people are ontologically different (flowers rejects that premise). They also neglect the always inherent and inescapable context of the covenant relationship. This appears to happen unawares, btw.