Edgy: "having a bold, provocative, or unconventional quality <an edgy film>"
DmC's story is the definition of trying to be "edgy". From showing Dante having a three way with prostitutes and having numerous ass shots in the opening to showing Lilith's womb exploding into "Little wet chunks". Almost everyone has some kind of abusive upbringing as a backstory, Kat gets tortured, civilians are shown to be executed right in front of you, you watch Poison's head get crushed and chopped up in a massive fan, you fight Mundus' unborn baby which is still attached to Lilith by the umbilical cord, you get dramatic close ups of Dante after he finishes slaughtering demons... I can go on and on. The game is in no way subtle about it's themes of anti-establishment, anti-consumerism, and anti-capitalism (gotta fight the man!!!!!!!!!!!!!!!!!!!!!!!!! Right?). They, for no apparent reason, feel the need to show Lilith taking it in the butt from Mundus for a good 20 seconds after already showing Dante getting a three way from prostitutes. And this isn't even getting into the satire found within the game (demons run the government; corporations want you fat, weak, and stupid; the Bill O' Reily and Fox news stuff; the fact that the game is "About how bad America has gotten"; etc). Again, DmC is the definition of trying to be edgy. It has nothing to do with the swearing, which I never brought up.
And all of this is fine and you are fine to like it. To me, it came across as juvenile as all of this stuff combined (yes, now I'll talk about the swearing since you brought it up anyway) with the gratuitous amount of swearing (even the walls scream "F*** YOU DANTE") happened in the span of less than an hour and a half (DmC actually doesn't have that many cutscenes). It was just a constant barrage of stuff added in for shock value that contributed little to the experience and had me rolling my eyes over half the time. Swearing is fine. Swearing like you are an 8 year old who just discovered that F***, S***, etc. are bad words and saying them is funny to you is just plain irritating.