I'll try to go a little more in depth
With series circuits, the current must be the same in each component.
With parallel circuits, the voltage must be the same in each component.
If we look at IV graphs for two hypothetical diodes, they might look very close at first glance:
But remember
we can only ensure the voltage is the same on each.
That means the current can differ by quite a bit:
Resistors have a linear IV graph (in accordance with ohm's law):
So we add one to each diode. This makes the curve more steep:
So if we look at the curve of the two hypothetical diodes with resistors:
This might look pretty much the same as what we started with, but since it's more steep:
The difference in current is substantially reduced.