Dear Sergio:

Let us look at the context of the discussion Jesus was having (John 8:30-44):

As he spoke thus, many believed in him. Jesus then said to the Jews who had believed in him, "If you continue in my word, you are truly my disciples, and you will know the truth, and the truth will make you free."

They answered him, "We are descendants of Abraham, and have never been in bondage to any one. How is it that you say, 'You will be made free'?"

Jesus answered them, "Truly, truly, I say to you, every one who commits sin is a slave to sin. The slave does not continue in the house for ever; the son continues for ever. So if the Son makes you free, you will be free indeed. I know that you are descendants of Abraham; yet you seek to kill me, because my word finds no place in you. I speak of what I have seen with my Father, and you do what you have heard from your father."

They answered him, "Abraham is our father."

Jesus said to them, "If you were Abraham's children, you would do what Abraham did, but now you seek to kill me, a man who has told you the truth which I heard from God; this is not what Abraham did. You do what your father did."

They said to him, "We were not born of fornication; we have one Father, even God."

Jesus said to them, "If God were your Father, you would love me, for I proceeded and came forth from God; I came not of my own accord, but he sent me. Why do you not understand what I say? It is because you cannot bear to hear my word. You are of your father the devil, and your will is to do your father's desires. He was a murderer from the beginning, and has nothing to do with the truth, because there is no truth in him. When he lies, he speaks according to his own nature, for he is a liar and the father of lies."

Some of the Jews listening to Jesus came to believe in him. But then Jesus demanded more from them that mere belief and a shallow enthusiasm. As the Navarre Bible commentary says:

...they should be true disciples; Jesus' words should imbue their whole life. That kind of faith will bring them to know the truth and to become really free persons.

The knowledge of the truth which Christ is speaking about is not just intellectual knowledge; it is rather the maturing in the soul of the seed of divine Revelation. That Revelation's climax is to be found in Christ's teaching, and it constitutes a genuine communication of supernatural life (cf. John 5:24): he who believes in Jesus, and through him in the Father, receives the wonderful gift of eternal life. Knowing the truth is, in the last analysis, knowing Christ himself, God become man to save us... This is the only kind of knowledge which really sets us free, because it removes us from a position of alienation from God -- the state of sin and therefore of slavery to the devil and to all the attachments of our fallen nature...

Many of the Jews found their pride under attack by Jesus. They did not consider themselves slaves because they were children of Abraham. Their belief in Jesus began to dwindle at the these words of Jesus. The Jews had a false security because they were descended from Abraham, thus how is it they are to be "set free" as Jesus said?

The Navarre Bible commentary explains:

Our Lord replies to the Jews' objection: (v 27-41) yes indeed, they are Abraham's children, but only in a natural sense, according to the flesh; this is something which does not count any more; what matters now is acceptance of Jesus as the One sent by the Father.

It is not only the Jews who have this false security, but some of us too. As the Navarre Bible commentary mentions:

The false security Jews felt on the grounds of being descended from Abraham has its parallel in a Christian who is content with being baptized and with a few religious observances, but does not live up to the requirements of faith in Christ.

This brings us to the verse in question. The Navarre Bible commentary explains:

...the attitude they [the Jews questioning Jesus] is in contradiction with this condition of being children of God -- for that should lead them to accept Jesus, since he is the One sent by the Father. Because they reject the only-begotten Son they are acting like partisans or sons of God's enemy, the devil. The devil, because he opposes our Lord, who is Truth, is the father of lies: by lying he seduced our first parents and he deceives all those who yield to his temptations and commits sin.

With this as a background the answer to your question is that Jesus says that the devil is their father because they reject the truth and accept lies. The devil is the father of all lies.

We too become sons of the devil when we accept lies. In this way, those who have received God's revelation, such as the Sedevacantist, Ultra-traditionalist, and Liberal Catholics, are all sons of the devil because they have accepted a lie over the truth of Christ and his Church.

We are not sons of the devil by mere sinning, that is, when we try to live a Godly life and occassionally sin and then go to Confession. We become sons of the devil when we choose sin over the Truth in an ongoing way in our lives and will not repent of it.

All those who live in concubinage (live together without marriage), or live in adultery (married person divorced from previous marriage but no annulment who remarries), or who fornicate and think there is nothing wrong with it, or those who contracept, or who believe in abortion, or sexually active homosexuals and those who believe that homosexuals may be married, and other such things, are all sons and daughters of the devil because they have given up the Truth, which is Christ, for a lie.

I hope this helps to understand the verse.

God Bless,
Bro. Ignatius Mary