Over the last months I've attended a grandson's siyum on Shas, another grandson's siyum on Shisha Sidrei Mishna, and a Chag Hasmicha at my son's Kollel, Kollel Horaah of America in Marlboro, NJ.
At every single event, someone said that saying Mazal Tov is out of place, because these occasions are the result of hard work and discipline and have nothing to do with mazal. You don't say mazal tov on Ameilus!
This has been attributed to the Briskers (an attribution that has been validated,) and (which I do not believe) to Reb Moshe.
Whoever said it, I, and Gandalf, disagree.
“Do you wish me a good morning, or mean that it is a good morning whether I want it or not; or that you feel good this morning; or that it is a morning to be good on?”
Mazal Tov is not a statement that what you have is the result of mazal, and it is not "congratulations". It is a wish and a bracha that you will have good mazal in the future, and that is very, very appropriate. When a person makes a siyum, or gets smicha, you are celebrating three things.
1. You join in your friend's happiness of a great goal attained after disciplined and dedicated hard work. You (if you are not suffering from ASD, or a psychopath who is indifferent to other's emotions) are happy that the other person has worked so hard and has accomplished something so precious.
2. You celebrate the new kedusha in the world. Unlike those that say "מאי אהני לן רבנן," you know that every talmid chacham that rises another darga of sincere Yedias HaTorah makes the world a better place and brings it closer to the Ribono shel Olam. That is a simcha for everyone!
3. A. Now that this person has finished a section of the Torah, the next time he learns it he will be learning a different Torah. אינו דומה! Anyone that has learned Eiruvin knows that after learning it once, you know very little. After chazering, it becomes a new masechta. Now that you've learned it, you need mazal and siyata dishmaya that when you learn it again, it will reveal its secrets and you will be zocheh לאסוקי שמעתתא אליבא דהילכתא.
B. Now that this person has assimilated a body of knowledge, and kal vachomer when he has hetter horaah, he has the opportunity to put his knowledge to use in his own life and in that of others. For that, you need mazal for siyata dishmaya that you should use it well.
C. When a person gets smicha, or learns a significant limmud, he is like a sefer Torah. He might have the opportunity to spread his knowledge, to teach, to influence, to be a leader. Or he might just go home and do nothing with all that he has. We all know there are great poskim and lomdim who are crowned Kings of the world, and others, of equal or greater stature, that have to stand in line to buy Challah erev shabbos and you can barely find a minyan for his levaya. What is the difference? Mazel! Even a sefer Torah needs mazal - one beautiful and holy sefer will lie gathering dust until it cracks and crumbles from age and disuse, and the other is used every krias hatorah. ( נשא קל"ד."תקוני הזהר צ״ט ב, "דכלא תליא במזלא אפילו ספר תורה שבהיכל) So if anyone needs the bracha of mazal tov, it is someone that finished a masechta or a new musmach.
This bothers me. How can the Briskers be so narrow minded that they don't realize that the mazel tov by a siyum is a blessing for the future? Bishlema when the Brisker Rov was told on a yortzeit that his father's neshama should have an aliyah, he got angry and said "Why are you saying that to me? Talk to the wall!" But a mazel tov by a siyum is treif?? I assume this is because the Brisker idea of a glorious future is that they emulate exactly and not one iota more their heroes of the past. Their future is the past. With that mindset, it is understandable that they interpret any good wishes by a siyum as an assessment of how well you've recreated the past, not a hope of dynamically achieving a fruitful and beautiful future.
I guess they hold that the Gemara in Megilla 6b,
גואמר רבי יצחק, אם יאמר לך אדם: יגעתי ולא מצאתי אל תאמן. לא יגעתי ומצאתי אל תאמן. יגעתי ומצאתי תאמן. דהני מילי בדברי תורה
means that all that matters is ameilus. But I can't see how that's possible. After all the ameilus, you need special mazal to become a marbitz Torah and be mechaven el ho'emes.
In any case, the mussar haskeil is that you can and should say mazal tov by a siyum and by a chag hasmicha. The Brisker Rov says No; Eisenberg, for what it's worth, says Yes. Just as by a wedding, you wish the chasan and kallah good mazal on the new world they hope to create, so, too, by a siyum and smicha, you wish the chasan haneshef good mazal with his new kedusha and Torah.