There are two mystical reasons why Christ did not want to be touched.
First, because this particular woman signified the Church of the Gentiles, which was not to touch Christ by faith until he had ascended to the Father: “A congregation of people will surround you; for their sakes return on high” (Ps 7:8).
The other reason is given by Augustine in his work on The Trinity. It is that touch is the last stage of knowledge: when we see something, we know it to a certain extent, but when we touch it our knowledge is complete.
Now this particular woman had some faith in Christ, which was that he was a holy man; and this was why she called him Teacher.
But she had not yet reached the point of believing that he was equal to the Father and one with God.
Thus Christ says, Do not hold me, that is, do not allow what you now believe of me to be the limit of your faith, for I have not yet ascended to my Father, that is, in your heart, because you do not believe that I am one with him – yet she did believe this later.
In a way Christ did ascend to the Father within her when she had advanced in the faith to the point of believing that he was equal to the Father.
Or, we could say, with Chrysostom, that after this woman saw that Christ had arisen, she thought he was in the same state as he was before, having a life subject to death.
She wanted to be with him as she was before his passion, and in her joy thought there was nothing extraordinary about him, although Christ’s flesh had become much better by arising.
To correct this impression Christ said, Do not hold me. It was like saying: Do not think that I have a mortal life, and can associate with you as before: “Even though we once regarded Christ from a human point of view, we regard him thus no longer” (2 Cor 5:16).
This is what he adds when he says, for I have not yet ascended to my Father. Accordingly, this statement does not give the reason for his prohibition, but an answer to an implicit question.
It was like saying: Although you see me remaining here, it is not because my flesh is not glorified but because I have not yet ascended to my Father.
For before he ascended he wanted to strengthen in the hearts of the apostles their faith in his resurrection and in his divinity.
Thomas Aquinas (1225-1274): Commentary on John, cap. 20, lect. 3, 2517-2518.