For what purpose? , a 2.5 year old thinks Bugs Bunny is real ... just not ready.
I received First Holy Communion in the first grade, at age seven. It was a solemn occasion that I remember well; boys wore suits & girls wore white communion dresses. As children we understood that we were receiving the Body and Blood of our Lord, for we had been so instructed for months before the holy event. Age seven is the age of reason IIRC.
THAT’s why Communion should not be given to two year olds.
The question hinges upon whether or not communion is a human act done by us for God (as, say, the Baptists believe), or a divine act done by God for us. If it is a human act, then it becomes part of the law, and not part of the gospel. But when Jesus proclaims "This is my body," He is also proclaiming that communion is a divine act. If it is therefore a divine act, then the cognitive ability of the recipient is not at issue, because it is an act of grace.
Would a Catholic church refuse communion to a 25-year-old whose cognitive abilities were of a 2.5 year old? I don't know for certain, but I don't think so--I know that LCMS Lutherans would not refuse solely on the basis of mental age. And I say this knowing that LCMS requires a two-year confirmation process that concludes at age 14 in order to receive communion, something with which I disagreed when both my children had to wait to receive communion until that age, though I made no stink about it at the time, except to admit my disagreement to the pastor in private. But I think the Orthodox have it right: if baptism is an act of God and communion is an act of God, then both should be available as soon as possible, and in the case of communion as often as possible, in the life of the Christian, whether incipient or self-proclaimed.