Resources for Chagigah 2
1. The משנה begins with the מצות ראיה in the עזרה. See תוספות here in ד"ה הכל who mentions that there are two separate parts to the מצוה: first there is the מצוה to show up in the עזרה during the רגל and second there is a חיוב הבאת קרבן. There is a very important רמב"ם in הלכות חגיגה פּרק א' הל' א who says that the מצוה of ראיית פּנים and the חיוב קרבן are so completely connected that if one comes to the עזרה on יו"ט without a קרבן, one fulfilled none of the מצוה and just got an עברה for coming to the עזרה without a קרבן! In other words, the הבאת קרבן is a תנאי in the מצות ראיה. See the טורי אבן who asks a question on the רמב"ם based on the following: תוספות (mentioned above) brings an important ירושלמי at the beginning of חגיגיה that says that our משנה which exempts women and children from ראייה is only talking about the חיוב קרבן. However, both men, women, and children are all obligated in ראיית פּנים in the עזרה. The טורי אבן reasons from here that if there are people who can have the חיוב ראיה but do not need to bring a קרבן (like women), then the מצוות cannot possibly be תלוי זה בזה. (The truth is that תוספות says that the בבלי doesn’t pasken like the ירושלמי, so the רמב"ם may be going like the בבלי.) See the אור שמח on that רמב"ם who says that the ירושלמי is actually a proof to the רמב"ם! The ירושלמי just says that children are חייב in ראיית פּנים and that this is learned from הקהל. The simple reading of it is that women are not obligated in ראיית פּנים (against the משמעות of תוספות). As such, there are no people who are חייב in one part of ראייה and not the other. Rather, the father just has the additional obligation to bring his son, but the son himself has no obligation to come as he is not a בר דעה. See the רידב"ז on the ירושלמי who adds that the ירושלמי cannot learn a חיוב ראיה for women from הקהל for the exact reason the רמב"ם said- since women don’t need to bring a קרבן they can’t be חייב בראיה. However, children never come for the מצוה itself—they just come to give שכר to the parents. As such they should still come for עלי-ה לרגל.
2. רש"י in ד"ה איזהו קטן says that the father and mother and obligated in the חינוך of the child. Whether a mother is obligated in חינוך הבנים is a מחלוקת ראשונים. See the תוספות ישנים in יומא דף פ"ב who says that women are not obligated in the מצוה of חינוך.
3. תוספות in ד"ה איזהו קטן says that even though a child can’t do the מצוה of סמיכה to his קרבן, it’s still counts for חינוך and the child must bring the קרבן. This seems unusual as the rule as to what age a child is חייב in חינוך for a given מצוה is when he can physically do the מצוה. For example, the age for a child to take the לולב is כדי לנענע בו (when he can do the נענועים). Moreover, see the חידושי הגרי"ז in ערכין פּרק בּ הל’ א that says that we see from לולב that the child must even be able to do the parts of the מצוה that are not מעכב such as the נענועים. If so, why is a child obligated to bring a קרבן ראייה for חינוך purposes when he cant do סמיכה? See the תהילה ליונה who suggests that the reason a child can’t do סמיכה is because since the סמיכה isn’t valid (since he’s a kid), he’s just being משתמש בקדשים. Consequently, he really could do the מצוה, we just don’t let him.
4. תוספות in ד"ה לישא שפחה says that we don’t say עשה דוחה לא תעשה by an חצי עבד to marry a woman since the לאו is from the time of העראה and the עשה happens only by the גמר ביאה. See the קובץ הערות in סימן כ"ט אות כ"ז who brings the מנחת חינוך who asks that even at גמר ביאה you haven’t had any kids so what would it help if the לאו only happened at גמר ביאה? He answers an important יסוד: it is not the קיום המצוה that is דוחה but rather the מעשה המצוה that is דוחה.