Why does the Pope include himself among the sinners? 'We are all sinners. But God heals us with an abundance of grace,
  mercy and tenderness.' (emp. mine)


the Holy Father, Pope Francis, said on Twitter. 

Why does the Pope say 'We are all sinners' clearly including himself among the sinners? 

As far as I know, it seems at least strange, if not absurd, that the Holy Father is a sinner, but I'm not an expert of these things and, perhaps, I'm not well aware about what sin is. 

In fact, to the best of my knowledge, I think that a sin is something that is against one or more of the ten commandments. But, if so, I cannot think of the Pope make something in disagreement to the ten commandments. 

Please, can anybody explain? (Peace be with you)
The doctrine of original sin says that every human being is a sinner.

Indeed, the Bible also says:

Romans 3:10


  As it is written: "There is no one righteous, not even one;


and

Isaiah 56:3


  All we like sheep have gone astray; we have turned—every one—to his own way; and the LORD has laid on him the iniquity of us all.


and Isaiah 64:6


  We have all become like one who is unclean, and all our righteous deeds are like a polluted garment. We all fade like a leaf, and our iniquities, like the wind, take us away.


Indeed, only Jesus escaped this sin - as Hebrews 4:15, in describing the uniqueness of Jesus writes:


  For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin.


Here, the obvious implication is that even High Priests (and their modern counterparts) sin.

Indeed, even the canons of the church explicitly clarify this point:


  Trent-Justification Canon 1. "If anyone says that man can be justified before God by his own works, whether done by his own natural powers or through the teaching of the law, without divine grace through Jesus Christ, let him be anathema."


With the possible exception of Pope Joan*, every Pope is man.  As man, he is subject to the same consideration.

The idea of total depravity and the universality of sin says that everyone (and that includes a Pope who knows his scripture well!) is both a sinner and under judgment.  Indeed, this idea gives birth to many popular sayings on the matter, such as:


A saint is just a sinner who falls down, and gets back up
Evangelism is just one beggar telling another where to find bread - D.T. Niles.


While it is tempting to chalk this up to humility the truth of the matter is that any priest worth his salt already knows this in his soul.

Oh, and finally, before you ask, yes, Pope Francis has his own confessor.



*The Pope Joan thing was a joke, in case you are wondering.