I used to have a theory about this on the Wheel of Time theory post.

When saidin is channeled it its diverted back to the True Source in a certain way, and saidar in another way. I think balefire resembles both saidin and saidar. The pattern therefore cannot deal with it, and the threads burn. That is why both male and female channelers can sense it in any form.

Some people think that Be'lal screamed because of the temporal nature of balefire. He saw his death. However, Moiraine clearly says that she senses the residues later in the series.