LED strip negative wire connected from the end
If you redraw your LED diagram to show the resistance of the wires (forget about the exact values, or the fact that the diodes shown are not LEDs, that's not important)







simulate this circuit &ndash; Schematic created using CircuitLab

then you will see that for a long string, if you powered them with both terminals at the D1 end, D1 would be bright, and the rest would get progressively dimmer.

If you power the string at opposite ends, the voltage drops across the sections of wire are equalised, and the LEDs get the same voltage. Each LED sees the same length of wire, the same resistance.