It's not a matter of prediction. What you call "the future", for a different observer moving at a different speed relative to you is "the present". You can't deny the existence of that observer's "the present" just because from your point of view that moment is in the future. Your point of view isn't special.
His present and your present are equally real; his happens to include parts of your past, present and future, depending on location.

There are moments in that observer's future that are on your present. Would it be reasonable for him to tell you "those moments in your present don't yet exist, because for me they are in the future". You would think him crazy. You could literally point at that moment in your present and say "it's right there, how can you tell me it doesn't exist?"