One of the aspects of Psalm 22 that doesn't get enough attention is how the psalm ends. The individual in the passage is approaching death (verses 15 and 20-21), apparently at the hands of the enemies mentioned in the psalm, who are likened to animals. He asks for deliverance from those enemies, but says nothing of deliverance from some other manner of death, like an illness. And he is delivered. We're not told how he's delivered, but we're told that he is (verses 22-24). Verses 27-31 refer to the major significance of what's happened, how people across the world will hear about it and turn to God as a result of what's been accomplished. Those verses refer to widespread influence both geographically and chronologically.
That's happened on a large scale with Jesus. There have been widespread discussions of his execution in Christian and non-Christian sources from the first century onward.
By contrast, none of the many records we have of David's life describe anything even close to what Psalm 22 depicts. It seems unlikely, given what we know of David's life, that events such as those described in Psalm 22 happened to him. So, a fulfillment in David's life seems unlikely upfront, and it isn't referred to elsewhere in the oldest records we have of his life. An advocate of David's fulfillment of the passage could appeal to the psalm itself as evidence, but the widespread influence described in the closing verses of the psalm make more sense if they refer to something that would be discussed elsewhere as well.
The Christian understanding of the passage not only has the psalm itself recording the events, but also has the events being widely discussed from early on after the events, both geographically and chronologically, in contexts independent of Psalm 22. The closing verses of the psalm make more sense under the traditional Christian understanding.
