Discarding the undesirable

This week I purchased a strainer to place over the drain in the kitchen sink. Coincidentally, the following day I received a daily halacha email from Rabbi Eli Mansour with the subject line of Pouring Into a Sink With a Strainer on Shabbat. The Rabbi wrote that "often, a liquid with large pieces is poured into the sink, and the insert catches the large pieces while allowing the liquid to fall down the drain. The question arises as to whether one may pour liquids into a sink that has such a contraption on Shabbat. The Shabbat prohibition of Borer forbids separating mixed items. When one pours a liquid with solid pieces into a sink, he in effect separates the liquid from the solid pieces, as the strainer catches the large pieces and removes them from the liquid. Seemingly, then, pouring into a sink on Shabbat would violate the prohibition of Borer."
The rabbi answered that, "in truth, however, it is permissible to pour liquid into a sink with a strainer on Shabbat, even if the liquid has solid pieces that will be separated from the liquid. One of the conditions for violating the prohibition of Borer is that one separates "Pesolet" - something which he deems undesirable - from "Ochel" - something which he desires. When a person pours something down the drain, his intention is to discard all of it - liquid and solid alike. Although he indeed separates the solid pieces from the liquid, he is not separating something he doesn't like from something he likes; he doesn't like either substance. Therefore, it is permissible to pour liquid containing solid pieces into a sink with a strainer on Shabbat, and doing so does not transgress the prohibition of Borer. This is the ruling of the work Shemirat Shabbat Ke'hilchata, and also appears to be the position of the Mishna Berura."