OK here's the truth. The electrical current does not...does not...flow from anode to cathode like they taught you in HS or in EE class. That plus to minus came from olden days (like the 1700s) when they had no clue which way it flowed; so they more or less arbitrarily set the flow to be anode to cathode.
And that worked because if you are consistent when working circuit problems, you can use either way, cathode to anode or anode to cathode, and get the same correct answers. But you have to be consistent, you can't change the stream in the middle of the problem.
But we physicists know the other half of the truth...the flow of electrons, called electron drift, is actually cathode to anode. And that results because the negatively induced field at the cathode does in fact push the electrons away with EMF.
So the answer to your question is simple. The push of the electrons is not in the opposite direction of the electron current. It's the engineering current that's in opposite direction of the real electron current. Real current, the drift, goes cathode to anode. ANS.