We have heard this expression "on-opposites" and maybe not been real sure what it was. If you have ever woven plain weave you have woven on-opposites. You weave one equal half the threads against the other equal half of threads. You may have put your threads on shafts 1 and 2 only for a two shaft weave or plain weave. You may have put half your threads on shafts 1 & 2 in the case of summer and winter. In that case you would weave shafts 1+2 versus all the other shafts. Or you have put your tie-up in a two-two twill.
If you have your tabby treadles tied up as above, to weave on-opposites, you will weave 1 versus 2.
On a four shaft loom with a balanced twill tie-up (2/2) is divided into two pairs.
Shafts 1 & 2 versus 3 & 4
Shafts 2 & 3 versus 4 & 1
The treadling order pairs up the two blocks or sheds that are the exact opposite of one another.
So you can think about weaving your plain weave web on opposites, or think about the different blocks you are weaving. If you want to weave on opposites ,or in pairs, you will need enough treadles where you have two different treadles for each block used.