Sorry for the "its" and "their"...

It derives from calligraphy, which was the driving stylistic element for the Carolingian Miniscule:

“The script ultimately developed from Roman half uncial and its cursive version, which had given rise to various Continental minuscule scripts, which were combined with features from the "Insular" scripts that were being used in Irish and English monasteries.”

The quill pen was cut so it provided a flat area. Due to the position of the right hand, the quilt’s tip was causing an angled stroke, which provided strong strokes downwards and softer strokes sideways, although the goal was probably to keep both strokes equal in force.

The minuscle “t” derives from the Roman Capitalis “T”, and the first stroke of the quill was downwards, followed by the second stroke sideways from left to right. Slight inaccuracy caused a little bump on the top where the T-downstroke began, which led to the slightly crossed shape. The sail shape in serif fonts, as you have shown it, is a result of both angled strokes melting into one area at some point of type development. Just like the curve at the bottom of the lowercase “t” and the lowercase “a” derives from swift motions when writing minuscule scripts.

Thanks.

The ‘sail’ origins in writing :–) as shown here. I prefer to write the horizontal stroke first (no matter if I write T or t). Doing so, I can more easily avoid the vertical stroke causing a bump in the horizontal one that the other way round. Also I think it it is easier to find the right starting point for the horizontal stroke than for the vertical stroke of T or t, because the further I am away from the preceding letter, the more I have to guess about the size of the inter-character space.