It’s because you don’t seem to understand what “Person” means in the doctrine of the Trinity.
It’s true that the word “Trinity” is not found directly in Scripture, but Christians don’t read the Bible in isolation. Christians have always read the Bible together with the guidance and collective wisdom other faithful Christians who are part of the universal church across the ages. The doctrine of the Trinity took several centuries to be fully articulated precisely because it is not easy to understand the witness of Scripture as One God existing as Father, Son, and Spirit. Since the 4th century, Christians have collectively agreed that the Trinity is the best way to take into account the full witness of Scripture regarding the Godhead. Thus it is in fact a very biblical doctrine.
Regardless of what you think, I strongly advise you to first seek to properly understand the doctrine of the Trinity before rejecting it as “unbiblical” or “man-made”. This chapter from Louis Berkhof’s Systematic Theology is a good start.