If a couple has a boy and a girl, thereby Halachically fulfilling the Mitzvah of Pru U’Rvu, then why is necessary to get a Heter for birth control?
See here for a thorough analysis of the parameters of this Mitzvah:
I am teaching a high school class about the Mitzva of Pru U’rvu. What is the Mitzvah M’doiraisa and what is the Mitzva M’derabanan? Please include which Pasuk we learn this from.
This link in itself deals with the basic premise in your question.
In addition to these issues relating to the actual Mitzvah of having children, there are other serious Halachic concerns with many of the methods of birth control.
Aside for all of this, the general idea of limiting the amount of children is inconsistent with the Torah view that every child is considered a Bracha from Hashem.
See below for a letter from the Rebbe about the topic. A sample representation of many such letters and Sichos.
An excellent compendium on the topic can be found in the most recent published book Shall We Have Another by Rabbi Mendel Dubov, available here.
“You inquire in your letter: since you already have two children — may they be well — and the doctor is advising you to practice birth control, what is my opinion in this matter.
You surely know that generally speaking, birth control is not consonant with the view of Torah, which views children as a blessing from G‑d — a blessing that G‑d bestows upon the parents.
The Torah also maintains that a Jew does not have strictly private concerns, as every Jew is part of the Jewish people as a whole and all “private” matters of each and every individual Jew affects the entire Jewish nation.
[This is] particularly so during present times, following the evil decrees and the Holocaust — may G‑d protect us — when so many millions of Jews perished in sanctification of G‑d’s name. [Thus, your not having additional children impacts not only yourself, but the entire Jewish nation as well.]
Nevertheless, in a situation where something can be detrimental to the health of a Jewish individual, be it man, woman or child, [then one may utilize measures that would otherwise not be undertaken], for the health of a Jew — to quote the Rambam — is “part of the path of the service of G‑d.”
[For this reason, when there are health concerns, then] in specific situations the Torah permits specific forms of birth control. However, it is difficult to offer a general directive with regard to the above, for it depends on the manner and degree of harm the pregnancy or birth will cause the mother, as well as the particular form of birth control used.
I would therefore advise you that after you communicate once again with your doctor and he advises you as to what form of birth control he has in mind, you should then turn to a chassidic Orthodox rabbi and hear his opinion. …
(Igros Kodesh, Vol. IV, p. 76)