Wait, what the f did I say? "Shouri" anime? What's a shouri? Did the Otaku Federation or more affectionately in some circles known as the NHK, and in the other circles/camps known as Genshiken coin this term? Or did Some overlords (Ahem The Third ahem) of this planet decided on that term? Did some secret Organization based in France (read: Le Soldat) planned this? Or is it just another marketing scheme by the horny and money grabby greedy directors at a studio by the name of Gainax (with the New Century Evangelion Scam)'? All right, all right, I'm over doing it…
Both styles of anime are well liked by many people, and these days, many anime simply combines these elements in order to attract men to watch them. In classic Shonen anime, there are usually a lot of fights that never end (ie, Dragon Ball Z fights, Yu Yu Hakosho arena duels), but there's another vein of Shonen anime, which delivers a lot of fan service – girls showing butts, parts of breasts, pantie shots and girls kissing.
Now girls kissing is almost always featured in Yuri shows, which are aimed at men. In Shonen shows, there are fights, and a lot of times, Mecha fights, anyway, Shonen shows features fights, mechas, and lots of fan service. In these shows above, we have mostly or almost only women as main characters. In classic anime, shows that only have women as main characters or shows that barely have a guy or two are usually shojo anime – Ace wo Narae, Marmalade Boy, Sailor Moon, etc.
Notice these shows don't feature one woman that fights like men or better than men (ala Revy from Black Lagoon), or women that does everything better than guys can do (Noir, Madlax, Tenchi). In these shows, with the Exception of Sailor Moon, women don't do that much except share feelings and fall in love. And Sailor Moon was weak to begin with. But anyway, these days anime seems to have this trend – featuring women and shows what women do or think, but placing them in a classically men-in-charge situation, or rather, Shonen situation – alien invasion, giant mecha fights, or situation where women would lose a lot of clothing or do embarrassing things (in Girls' High/High School Girls where the girls explore the girls' locker room, and find some rather feminie-nasty things there, and the shots focus on their panties when they climb into the school, and doing other stupid things). It's almost like since male Otakus love seeing women doing silly/embarrasing/sexy/lesbian things, why not feature only women and have them do these things? It's almost like lesbo porn, except these shows don't go that far – and they have real plots! Oh and in addition, some of these shows features giant mecha fighting, emotional conflicts, and hot-blooded action! All with either just women, or at least very few men. Hence this term was coined:" Shouri anime." Oh, and it sounds better (at least to us) than "Yunen anime."