Based on your answer I can see a sort of selfishness, I don't know how else to put it.
So why are Jewish missionaries looking for Jews? There are chabads in certain areas of the United States that do indeed look for Jews. Not non-Jews. But they do look for those born Jews apparently seeking to bring them back or bring them to a more religious life than they have. Why do you feel that is?
P.S. if someone else's religion is ok because it makes sense to them, I wonder if you think it makes sense to the God you claim to worship.
The answer to this is very simple. Hashem, in the Torah, never gave a directive that Jews were required to make the world or convince the world to be Jewish. From the Torah, the requirement for the non-Jewish world is to keep the 7 Mizvoth of Noah. (6 Mitzvoth from Adam and 1 from Noah).
The additional mitzvah that Avraham received for brith milah was never a "requirement" for the rest of the world to take on UNLESS they wanted to of their own free will. That is why one does not find that the only time Avraham sounght out people to join him was in Haran when he was about to enter into Kanaan. After that one finds that he and his children were verty particular about who could even marry into their family.
From the Jewish mesorah Avraham and his descendents had no problem talking about Hashem to the nations, and explaining the 7 mitzvoth but they did not go out and try to convert people to them.
So, when the Torah was given at Mount Sinai there was further no requirement for non-Jews to covert and become like Jews. Thus, the Torah describes a non-Jew who is allowed to live in the land of Israel as a (גר תושב) Geir Toshav i.e. a non-Jew who has taken on/accepts the 7 mitzvoth and thus is allowed to live among Jews in the land of Israel when there is a Torah based country.
So, if a person were to complain that we Jews are not out in the world trying to convert the world they must take that up with Hashem because at the end of the day a non-Jew who keeps the 7 Mitzvoth of Noah has a place in the world to come and is pleasing to Hashem. Even those non-Jews who do not and who have not followed what the Source of creation has established to be the truth do not go and burn in a lake of fire when they die. This concept is not found in the Hebrew Tanakh. Further, there are some people in the world who don't want to keep the 7 mitzvoth so we have no command to force them to do so. That is between them and Hashem.
Further to the above, for the last 1,800 years or so MOST of the non-Jewish world has not wanted to be Jewish; with some exceptions such as the Berbers of North Africa and the Himyar empire in southern Arabia/Yemen. The reason being that when Jews were dispersed throughout the nations and disposed in many places most people would not want to join what they perceive to be the losing side. Jewish law even takes this into account in stated that convesions cannot be done for the sake of getting a better situation when Jews are doing well but must be done for the sake of Hashem and the truth; or to say the realization that the Torah is the truth.
It is thus the job of every Jew to stand up for the truth, to live the truth, and the prophets claim that by doing so as a nation in the land of Israel one day the "Era of mashiahh" will happen. It is for this reason the Torah is very clear that Jews have a mitzvah/requirement to try and return every Jew to the path of the Torah; IF one is able to. Thus, organizations like Chabad, Esh HaTorah, Shofar, Hidabroot, etc. have been working to try and show Jews who were lost to the Torah the way back; if they so desire. This mitzvah in Hebrew is called, (הוכח תוכיח את עמיתך) and is found int he Torah in Wayiqra 19:18 and 19:17.
Lastly, there have been moments in history where non-Jews have either become Noachides, those who keep the 7 mitzvoth, because of Jewish influence or inspiration and also some have converted to the Torah for the same reasons.
For more information, see the following videos.