2. Question: If the Shulchan Aruch (Orach Chaim 673:2) says that the lighting if the Chanukah lights is what does the mitzvah then why do you have to relight without a blessing if you blew it out on purpose though you don’t have to relight at all if you blew it out by accident and certainly if it went out itself?
A. The Mishna Berura (25) adds that if you lit it in a place which will automatically go out like in a windy area then you should relight it in a proper area (that can potentially allow it to stay lit for 30 minutes.)
B. The Mishna Berura (26) says that even on eve Shabbos if it blew out before sunset you technically still don’t have to relight because the rabbis enacted the mitzvah to be done with a blessing in a fashion that the mitzvah would start before sunset though on all other days it should be lit afterwards.
Answer: The Avnei Nezer says that since he lit with proper intent then blowing it out by accident, without intent can’t nullify the lighting that was done with proper intent. But when blowing out on purpose and with intent then you are nullifying the act of lighting. Rav Moshe Feinstein explains that since you blew it out on purpose the one seeing that will say it was originally lit for his own personal need, why else would he blow it out. It’s the samething as lighting outside and the bringing the menorah inside where the Mishna Berura (675:1:5) says you don’t fulfill your mitzvah because people will say you lit for your own need, not for the sake if the mitzvah. (See Dirshu Mishna Berura 673:3 note 40)