What is the number one cause of current animal extinctions?

If you were asking for main reason for mass extinctions in general, I would say that it is abrupt climate changes.

However the K-T mass extinction was a consequence of a major comet/asteroid impact, and perhaps the Ordovician-Silurian mass extinction (the second largest mass extinction after the Permian extinction, the «Great Dying») could have been caused by a Gamma-ray burst from a supernova (or hypernova) explosion thousands of light-years distant, or could have been the outcome of the most severe glaciation of the Phanerozoic eon.

The most severe of all mass extinctions was the above mentioned Permian mass extinction, and the reasons for such a catastrophic event are not yet fully understood.

But you asked which is the main reason for the CURRENT extinctions. Indeed the scientific community believe that we are now watching a new MASS EXTINCTION, not just the extinction of a limited number of species.

I am sorry to say that I, personally, believe the reason is human beings.

And I know well this is currently a matter of debate and vigorous scientific and political dispute, due to the monstrous profits of polluter industry, along with the big bank's investments and the high finance lobbies supporting these industries.