Zevachim 5b - Lishma by Goat of Nassi

The gemara says that the passuk of "chatas hu" which is written in the context of the goat brought by a nassi, is the source that it must be shechted l'sheim chatas, otherwise it would invalidate the korban entirely.

The Meshech Chochma (Vayikra 4:22) questions, why specifically in the context of the goat of the nassi does the Torah decide to teach us the integral need for lishma by a korban chatas, rather than telling us this by a regular korban chatas? He explains based on a gemara in Sota 32b that the Torah tells us that a korban chatas should be slaughtered in the same place that the korban O'lah is shechted, so as not to embarrass one who brings a chatas by fooling bystanders into thinking he is actually bringing an o'lah. The gemara says that even though and o'lah is male, whereas chatas is female, it can be covered with the tail. If he chooses to bring a female goat, which has no tail to cover up the gender, that was his choice to embarrass himself, but wasn't compelled by the Torah. The Meshech Chochma suggests that it is for this reason that a Nassi brings a male goat, is to protect his honor so that people will be fooled into thinking that he is bringing an o'lah rather than a chatas. It would degrading for klal yisroel to publicize that a nassi did an aveira for which he has to bring a korban, so bringing a male goat is a method of limiting the chilul hashem. Therefore, one may have thought that the lishma on this korban should also be done l'sheim o'lah rather than l'sheim chatas so that everyone including the kohanim bringing it (and anyone listening according to those who say that lishma must be spoken out - see tosafos 4b, tosafos 2a and gilyon hashas). It is for this reason that the Torah writes "chatas hu" - it must be done l'sheim korban chatas and NOT l'sheim korban o'lah.

The fundamental point of the meshech chochma that a Nassi should hide the fact that he did an aveira and fool the bystanders into thinking he is bringing an olah rather than a chatas seems to me as being incompatible with the gemara in Horiyos 10b - אשר נשיא יחטא- אמר ר' יוחנן בן זכאי אשרי הדור שהנשיא שלו מביא קרבן על שגגתו, אם נשיא שלו מביא קרבן צריך אתה לומר מהו הדיוט, ואם על שגגתו מביא קרבן צריך אתה לומר מהו זדונו

The gemara indicates that when people see that even the Nassi is willing to admit his mistakes and bring a korban, they will be inspired to do teshuva. This seems to indicate that we want to publicize the fact that the Nassi is bringing a korban on his aveira, not hide it. The meshech chochma (4:31) himself acknowledges that for a regular person it is beneficial to embarrass himself by bringing a female goat and publicize that he did an aveira and that is why the Torah writes ריח ניחוח only in the context of a goat brought as a korban chatas, not a sheep. Only when he goes out of his way to embarrass himself over the aveira is his korban worthy of being a rei'ach ni'choach to Hashem. It is only by the Nassi that the Meshech Chochma suggests that it is beneficial to hide his aveira - but based on the gemara in Horiyos it seems that even a Nassi shouldn't hide his aveira.