This can be a few reasons: first, the paint may be too thin, not mixed up enought, or just junk paint.
second, its the wrong brush. I assume youre using latex paint - and I like Purdy, its my favorite brush, but I'm not sure of the (Nylox Sprig). I just get Purdy angled brushes that say "for all paints" on it, oil or latex. The brush should be whitish, not black bristles.
Finally, it could be the finish of your trim, and the "flat" your using now. Usually, doors and trim are painted with "semi-gloss" paint, and these look nice, but are hard to paint over sometimes, especially if your changing the finish to flat, and/or changing the color makes it even worse. Semi-gloss paints go on a little thicker than flat paints.
One more thing, I noticed you said you're applying paint with 1 stroke, then back-brush it once? This is not really how most people paint. You have to get that brush wet and paint small sections with many forward and back motions till it covers, sometimes going back over your work, re-dipping paint, etc.