Why do most historians argue that modern European history began in the 15th and 16th centuries?

Answer 1

several reasons

- fall of constantinople in 1453 marks the end of the 'east-roman -empire'

- columbus landed in the caribbean ..

- technical advancements

- printing press (gutenberg)

there may be other reasons but all together enabled europe to play a dominant role in world history for looong time.
before all that happened for example the islamic world and china were more advanced in some fields. (think of sciences like maths and astronomy etc.. or the large chines fleets which explored wide area around china long time before european vessels did the same)

Answer 2

C15th-C16th is the period of the European renaissance where we see acceleration in development and learning. The percusor to this era is the Dark ages when most of Europe is in upheavel and suffering greatly from war, disease, famine etc. This is not a period of learning or growth.