Think of the electrons moving along the dipole.
At the ends the current must always be zero because there is no place for the charge carriers to flow to.*
The maximum current must happen in the middle because the electrons going from one end of the dipole to the other must flow though the center to get from one side to the other.
Here is a nice animation from another Stack question....
If you want a deep intuitive understanding of this stuff I recommend you take a look at Matter and Interactions...
This book changed how I think about electromagnetics and resolved many long standing confusions I had.
*Assuming the tips are isolated in a vacuum and the voltage at the tips does not exceed the work function of the wire, which is a fair approximation for our purposes.