I held off on answering this question because the inclusion of WWII as a period where men were encouraged to knit threw me off. However, I'm fairly sure now that while some soldiers knit while not actively fighting or while prisoners of war in order to pass the time and to provide themselves with needed socks and scarves, men on the home front were not being encouraged to knit for the war effort during the 1940s.

The answer is something that really fascinates me. Effectively, while the present-day view of the Victorians and the twentieth century is that the former had extremely strict gender roles that were gradually rolled back over the course of the latter, in actuality the early twentieth century saw many soft gender barriers become much more strictly enforced. (Another example is the acceptability in the nineteenth century of two women being exceptionally close friends - potentially lovers, although proof of that kind of relationship would have been deliberately kept secret from contemporaries - and living together, which became socially unacceptable in the early decades of the twentieth century.)

Before and during World War I, knitting was certainly a feminine craft. At-home garment-making and -adorning was seen as women's work: sewing, crocheting, embroidering, tatting, and knitting were all types of needlework that women were expected to either know how to do or at least take some interest in, and men were expected not to know much about them. As a result, men knitting for the war effort needed to be quite secure in their masculinity, and newspapers and maagzines that reported on them made it very clear that they were MANLY men despite their knitting. For instance, they'd specifically share images of firefighters and trolley-car operators doing their part, described with adjectives like "husky" and "athletic". A teacher noted in one article that the boys in her class were happy to knit, right before going outside and playing "the roughest game of football imaginable". In a younger class, the boys were at first reluctant to be "sissies", but when the teacher told them that the girls were being more patriotic, they gave in, eventually becoming known as the Rocky Mountain Knitter Boys.

This is quite similar to how vaudevilian female impersonator Julian Eltinge was handled at the same time - he made a point of emphasizing his own masculinity when off-stage, aggressively threatening to punch men who made comments about him, and journalists followed his lead in reporting on his burly charms. It's quite likely that if these knitting men and boys were simply working for their own amusement, the papers wouldn't have been nearly so complimentary.

Other men were also taught to knit for the troops, ones who were more marginal to the ideal "husky", respectable, middle/working-class man. Patients in sanitaria, residents of almshouses, convalescing soldiers, and convicts also became involved in this effort, with less emphasis in the sources on how manly they were despite their feminine pastime.

After the war, society slowly became more and more rigid in its gender roles all the way through WWII and after it. The Average age at first marriage descended for both men and women and young women in college were more strongly encouraged to think about their marital prospects rather than their careers (as I discussed in this past answer on post-WWII Rosie the Riveters); housewives were seen as more and more decorative (as I discussed in this past answer about the declining position of the housewife). This is also around the time that pink and blue became cemented as girl and boy colors, respectively. Thus knitting on the 1940s home front was restricted to women and girls, because even emphasizing how athletic and strong male knitters were would not be enough to combat the stigma of taking on a feminine role.