FPS game where skill really matter.

IF we are talking about multiplayer, definitely Insurgency and forementioned CS:GO. Maybe if you like oldshool action, Rise of the Triad? But i don’t know what player base is like nowadays in that game. Also there is that free Quake in browser that has huge playerbase.
In singleplayer you are screwed these days. The only one i can think of is Takedown: Red Sabre, but reviews for that one are terrible. Maybe Painkiller : Black Edition on higher dificulties can fill your taste buds.

Battlefield 3 MP

Delta Force ^^

Insurgency.

Give painkiller a spin.

natural selection 2 :)
and day of deafeat: source

Killing Floor!

If you didn't played it, then try CS:GO.
Then I would recommend Tribes: Ascend, but I don't play it for almost a year already and the community was already small, but if you live in Europe or USA I guess you will find active servers to play. This is really a game about skill, if you never played a Tribes game the gameplay is different to what you're used to in any other FPS, but the learning curve is big, big, big...

The Arma games are pretty realistic, so I would say that would require a lot of skill not usually needed in CoD or BF. Rising Storm/Red Orchestra 2 should be right up that alley as well.

That's stupid. Call of Duty and Battlefield may be shit games with less substance to them than the empty void of the Cosmos, but skill still matters. If you're good, you're good, if you suck, you suck. That doesn't change, regardless of the game. Sure, the difference of value between players can be widened by a harder to learn game, or thinned by an easier one, but at the end of the day, it's all about pointing the cursor and shooting, whether it's old school games like Half Life or Unreal Tournament or new-age military realistic bullshit like Call of Duty. You can try those two I mentioned, but good luck finding someone to play with.

Fistful of Frags, Hard Reset (on hardest difficulty) and CS:GO but it seems like you already know it.

Insurgency.

Quake Live and Tribes: Ascend.

Hello Kitty Online

Firefall. Keep watch around the end of this month.

Quake Live

Strike Vector

Insurgency and all Counter-Stike games.

Red Orchestra?

Planetside 2 ?

tom clancy's rainbow six siege maybe in 2015 :D

Go for Arma games, or Red Orchestra / Rising Storm.