Does this article destroy the matriachal principle in Judaism?

No

There is a baseline failure by the writer to understand the meaning of the Halakha.

The key to understand is that "matrilineality" is a smelly red herring.

It is not about matrilineality -- it is about birth of the child into its family and into its nation.

A valid Jewish marriage is one "according to the laws of Moses and Israel" -- ie: BOTH participants must accept those laws -- ie: BOTH participants must be Jews (whether by conversion or birth is not important).

The pairing of a Jew and a non-Jew therefore has no Jewish status --

therefore, the father has no Jewishly legal claim on the child.

Therefore -- the child of a Jewish woman is definitionaly born within her family's Jewish household,

and likewise -

the child of a non-Jewish woman is definitionaly born outside of the Jewish nation.

Any Jewish father who makes the claim to force the child of a non-Jewish woman into the Jewish nation is therefore essentialy guilty of kidnapping.

As for the child him/her self --- then like any other non-Jew, he is free to enter the Jewish people according to the laws for entering into the Jewish people.

If the non-Jewish mother is interested in her child being part of the Jewish people, then she must first enter the Jewish people.

No

There is a baseline failure by the writer to understand the meaning of the Halakha.

The key to understand is that "matrilineality" is a smelly red herring.

It is not about matrilineality -- it is about birth of the child into its family and into its nation.

A valid Jewish marriage is one "according to the laws of Moses and Israel" -- ie: BOTH participants must accept those laws -- ie: BOTH participants must be Jews (whether by conversion or birth is not important).

The pairing of a Jew and a non-Jew therefore has no Jewish status --

therefore, the father has no Jewishly legal claim on the child.

Therefore -- the child of a Jewish woman is definitionaly born within her family's Jewish household,

and likewise -

the child of a non-Jewish woman is definitionaly born outside of the Jewish nation.

Any Jewish father who makes the claim to force the child of a non-Jewish woman into the Jewish nation is therefore essentialy guilty of kidnapping.

As for the child him/her self --- then like any other non-Jew, he is free to enter the Jewish people according to the laws for entering into the Jewish people.

If the non-Jewish mother is interested in her child being part of the Jewish people, then she must first enter the Jewish people.

===

EDIT

to your aditional details --

The final Halakhic argument is simply that the Halakha is that the child of a mixed relationship is defined according to the mother.

Therefore, there is at least two thousand years of presumption of error against the writer of the article.

But --

My argument in explanation of the Halakha, in case you missed it,

is that since there was no valid Jewish marriage, the alleged father has no valid Halakhic claim to the child.

He has humanitarian obligations to the child and mother - but no claim.

The author of the article misses because every Biblical argument he can possibly bring comes from valid mariages.

In a vaid marriage, the wife leaves her parents' household and becomes part of the husband's household.

Meanwhile the counter point from Ezrah-Nehemiah is precisely that the Jews who had taken foreign women in Babylon against Jewish law (presumably under some "secular" Babylonian marriage law) are required to send them off -- they have no right to take them or to their children.

I should add a few things to note that while it has been established in Halacha (i.e. it is not something that is controversial or something for which there is reason to be "lenient") that matrilineal lineage determines Jewishness, the author is not merely confining himself with pointing out what he disagrees with, he also has to say things such as:

"Those Rabbonim who exclude those who, according to Torah, are part of the community of Israel via the qualifications of the census are committing an aveira by transgressing the commandment..."

So, in other words, he is also condemning them for committing a sin for going according to Halacha!

He further says that:

"Joseph, Moses, Boaz all married foreign women. "

Without mentioning that a) Joseph and Moses married before the giving of the Torah and b) Ruth converted to Judaism (and in fact, she is held as a prototype convert).

Thus, it seems to me that he is more interested in engaging in polemics than actually addressing the issue he claims to want to discuss.

(Also, as another example, he goes on about how people of Yeshivot have an attitude "not to question"... etc. Translation: "Don't mind what those Yeshiva people have to say, they are not open minded enough...")

I should also note that in Halacha there is a difference between "who is a Jew" and "what a person's lineage is". For example, a person is a Levite because his FATHER was a Levi yet he is a Jew because his mother was a Jew. The person seems to try to argue that they are one and the same. He didn't seem to address that.