Well said! However there is a position between Arminianism and Limited Atonement.
God's omniscience requires that God knew before He created Adam that Adam would eat the forbidden fruit.
We are told in passed in 2 Pe 3:9
9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
KJV
We know from Rv 19:6
6 And I heard as it were the voice of a great multitude, and as the voice of many waters, and as the voice of mighty thunderings, saying, Alleluia: for the Lord God omnipotent reigneth.
KJV
That God is able to order and arrange things according to His will.
What then can explain why omnipotent God would allow His will, as expressed in 2 Pe 3:9, to be thwarted?
The only explanation that makes any sense Is that God wants something else more than He desires that all should come to repentance; which could not be possible if all were caused to come to repentance.
We see in Mt 22:36-40
36 Master, which is the great commandment in the law?
37 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind.
38 This is the first and great commandment.
39 And the second is like unto it, Thou shalt love thy neighbour as thyself.
40 On these two commandments hang all the law and the prophets.
KJV
That God places great importance on man having capacity to love. If man did not have the capacity to love, neither of the two primary commandments would have any meaning.
It is the nature of love that love cannot be programmed and must be volitional.
God's desire for a creature with the capacity to Love required that He accept a creature with the capacity to spurn and reject love. Even God's omnipotence can not overcome an inherent contradiction. Nothing can be white while it is black' or true while it is false.
God allows man to have the capacity to sin in order that he might also have the capacity to love.
Jesus took upon Himself the consequence of all men's and all women's sin in order that every person would once again have the capacity to receive and return God's love or reject it for him/her self.
God, being indeed sovereign, can base His election of who will be saved on any criteria of His choice; or even on His whim.
I believe that God has chosen to base His election on how each person responds to what Jesus has done for him or her.
A person cannot will himself/herself saved without accepting Jesus claims of Lordship (Ownership) over his/her life.