While I know people like Supermodel from Paris and Fatmanonice will rip this text apart and say everything is wrong, or the majority will simply ignore it, I've made a little write up.
Long text is long:
Playing a game competitively - this means any game - means that you want to determine skill between several players, usually two or a team of equally amounted players facing each other. Determining skill needs an environment that is the most even and balanced as possible. That is the general concept of competitiveness. I'm sure you understand that concept, that generally, a competitive game seeks balance in between the players so actual skill is determined.
In video games, especially fighting games, game balance is very difficult to achieve. Due to characters having different movesets, traits and other things such as special mechanics (e.g. the Aura of Lucario is a perfect example for that), there will be characters that are advantaged over others. Characters so have strengths and weaknesses, and it's up to the player of a character to cover the character's weaknesses with their strengths, while their opponent tries to exploit the weaknesses of that character.
Perfect balance is literally impossible with a cast of more than 1 character. While it can be extremely close to be completely balanced to the point where every character's matchup to each other has only so small advantages/disadvantages against each other that they are neglectable and able to be called even.
However, most fighting games aren't that balanced as I said, especially with a cast that has more than a small handful of characters. There will be characters that have a major advantage over other characters. Some characters have so many strengths that they have no problem in covering their weaknesses, thus doing very well against most of their opponents, while some characters have so many weaknesses that they can't cover them anymore and are victims to huge exploits of them.
If you have understood these paragraphs explaining the concept of competitive fighting games so far, you might be able to conclude the next line of explanation - regarding Smash - yourself.
Due to the unusual nature of Smash (it not having health bars and the players having to ring-out their opponent in order to win, etc.) and the fact that stages influence the performance of players and characters in this game series, the system of "Counterpicking" (I'll add Stagestriking into it since it's kindasorta part of it) has been introduced.
Counterpicking and Stagestriking are options given to the player to put themselves into a favourable position. They are neither absolutely necessary nor does the player HAVE to use counterpicking or strike a stage. However, they can put themselves into a favourable position by doing so, covering some of their character's weaknesses and/or being able to exploit the opponent's more with the help of a stage, and removing a stage that exploits their character's weaknesses by striking it.
Just like Gimping, Edgehogging, Camping, Chaingrabbing, etc., Counterpicking is an option given to the players. They don't have to use it, but usually, it's not a bad idea to do so.
Now, the thing is following: A favourable position does not mean an advantage only. There is no need to put yourself into an advantage, because in order to determine skill, an even position is all you need. An advantage over your opponent is favourable, but not necessary in order to determine the skill between you and your opponent.
If you are in an even matchup and you lose, nothing is to blame but yourself, since especially in an even matchup, there's nothing that counts more than your own skill and knowledge.
Too many people are focussed on thinking that counterpicking has to do with disadvantaged matchups, but that's wrong, since an even matchup is the only thing you need.
Now, let's take the following scenario. You main Dedede. Your opponent mains Falco. You play the first round. You lose due to the matchup. Now you get to counterpick - your opponent will first choose a new character if they do, then you can change your character, and then pick a stage to additionally put your opponent into a disadvantage even further.
But you are given the chance to at least make it even!
If you win this match, your opponent is able to counterpick you now, including character picks. Sucks, right? Because he will put you into a disadvantage, but at the very least will try to make the match even.
Take another example. You main R.O.B.. Your opponent mains Meta Knight. The same scenario occurs. You lose due to your matchup. Now you get to counterpick with a character that goes even with him and can win the match because of your skill - should it be there. Yaddayadda. If you lose, noone is to blame but your own lack of skill.
Let's take a really different example, because this time it'll run different. You main Diddy, your opponent is Meta Knight again. Diddy goes even vs. Meta Knight on pretty much every Neutral (you still can strike out Yoshi's Island, which is the Neutral he doesn't perform that well on). If you lose in this even match with Meta Knight, then there is noone to blame but yourself. There's a reason that this matchup is even, after all.
Now, let's assume - You are the better player, you win.
Meta Knight will now either take you into a stage that's better for him, or counterpick you with a character, additionally, let's say Snake. Now he wins.
Now it's your chance. He either changes his character to someone else or stays Snake, then you can counterpick that character. If he switches to Meta Knight, you can counterpick him too, because you can put Meta Knight into an even matchup, which means that if you lose, nothing is to blame but yourself. You now can pick Diddy again and go to another Neutral, for instance. Or play another character Meta Knight goes even with. Or you take Meta Knight to a ditto. Whatever floats your boat.
If you now say "But why do I have to play a character that goes even with Meta Knight?", then you don't understand why the Counterpick argument is flawed.
If you play a character, this character will have bad matchups with other characters. If you play Diddy and your opponent counterpicks you with Snake, you will have to have a character in your armory that can deal with Snake. If you play Dedede and your opponent counterpicks you with Falco, you will have to have a character who can deal with Falco.
Meta Knight is not an exception. He's just really really good, and therefore has advantages over most of the cast. That means you will have to have a character that can deal with Meta Knight. Just like you will have to have a character that can deal with your main's other bad matchups.
Of course, Meta Knight is always a safe choice, since he goes even with others at worst. But that doesn't mean that he breaks the option of counterpicking, because you can counterpick him to make the match even. That just means that Meta Knight is a really really good character. You will always have to be aware of the fact that you could run into a Meta Knight, just like you have to be aware of the fact that you can run into Snake, Falco, Dedede and whomever else there is in the cast.