In Matthew gospel, Why is Jesus falsely added to Joseph's line, Since Joseph(according to the story) is not the natural father?

Adoption and acknowledgement as his heir.

Joseph was his legal father.  That standing was not dependent on biology.

He's not "falsely added".

The wording is precise:

- Jacob was the father of Joseph the husband of Mary, by whom Jesus was born, who is called the Messiah.

In ancient Jewish culture

***as traditionally in our culture***

when a woman married

**she became a part of her husband's family**.

Therefore

any children she birthed after being married

**were deemed to be children of that same family**

that is to say: the husband's family.

We

in our culture

signify this

by the woman changing her family name to that of her husband.

In the New Testament period and culture

the Jewish people in the Levant did not use family names

(at least: not the commoners)

and so that family name custom was not followed

BUT the custom of perceiving the wife as belonging to the husband's family

remained

(and, indeed, in many ways, definitely not in all ways, the wife was perceived to be the *property* of the husband, not just a member of his family).

Joseph was the legal father.  Luke's account shows the family line through Mary.

Joseph's line is that of an "in-law" (as supposed).

Anonymous is lying! Ask any rabbi about Jewish law or "Hebrew law" whatever this person meant by that. Ask where did he get his information? This person claims to be an expert on Judaism and Jewish beliefs so ask where is this Hebrew law and how can I find it? I guarantee this person will not direct you to any honest or truthful sources if he gives an update/answer at all. 

Ask for an example of when an adopted child EVER became a cohen-priest? EVER became an Israelite and took on the father's lineage? It NEVER happened. 

'I say it is true because I wish it and therefore you should believe me even though I just made it up and I am either delusional, lying or don't know myself but need people to not lose faith in JC!' is what anonymous is more or less saying. 

Indeed you are correct. JC is falsely added to Joseph's geneology as though he is his real son. Lineage is a chain, either the chain keeps growing or it ends. Read the bible. Converts cannot claim to be descended from king David neither can priests of levitical descent. God swore to king David that he will NEVER deny or prevent king David's descendants from ruling on the throne forever i.e. his lineage or bloodline would never end. It also means that king David will always have a living descendant as long as the Jewish people exist. 

Psalm 132:11

The Lord hath sworn in truth unto David; he will not turn from it; Of the fruit of thy body will I set upon your throne.

Psalm 89:35

I will not violate My covenant or change the utterance of My lips. Once and for all I have sworn by My holiness— I will not lie to David— his offspring shall endure forever, and his throne before Me like the sun,…

Christians like to interpret offspring in the singular and not the plural tense. The Hebrew for multiple offspring is "Zaro" and singular is "Zera". Clearly the Psalms is not speaking about one man siting next to God in heaven forever. But you can see how Christians manipulate, twist and re-interpret scripture. They cannot accept the Jewish interpetations and translations because it doesn't match with their own invented criteria so that have to change the meaning of words and the order and context and play with syntax to get a twisted rendering. 

Both lines come from King David hertiage

Under Hebrew law, adoptive sons were entitled to their adoptive fathers inheritance. Joseph descended from King David giving Jesus then full legal rights to Davids throne. 

Joseph and Mary went to Bethlehem to be counted in the census. They counted Jesus as Davids son. They couldnt tax God.