All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
You mentioned that your husband is a good man, and this is a good and commendable thing; all praise be to Allaah for that grace. His protective jealousy over you is probably an indication of his love. However, it should be noted that the husband is advised to avoid excessive jealousy; moderation is required in order for the protective jealousy to be praiseworthy. Please refer to fataawa 156495 and 90757 about the praiseworthy and blameworthy jealousy.
You should know that the husband has the right to prevent his wife from going out of the house without his permission and that she is obliged to obey him in this regard, except for a valid necessity. This is proven by the hadeeth narrated on the authority of Ibn ʻUmar in which the Prophet, sallallaahu ʻalayhi wa sallam, said, “Do not prevent the female servants of Allaah from visiting the mosques of Allaah.” [Al-Bukhari and Muslim]
Al-Baaji wrote:
“The hadeeth indicates that the husband has the right to prevent his wife from going out of the house and that the wife must have his permission before leaving her house. If the husband had no right to prevent his wife from going out of the house without his permission, then the hadeeth would have addressed women directly to go out, and it would not have addressed men not to prevent their women from going to the mosques...” [Al-Muntaqa]
Hence, your husband is entitled to prevent you from going out of the house for teaching or carrying out any other activity. However, if you had stipulated a condition that you would work outdoors after marriage when concluding the marriage contract and he agreed on that condition, then he is obliged to abide by that condition except due to a sharee'ah-acceptable excuse. Please refer to fatwa 224677.
In any case, we advise you both to try your best to reach mutual understanding and trust; the husband should not prevent his wife from going out when she needs to as long as she would not go to places fraught with doubts. Moreover, you should not go out of the house without his permission and should not turn it into a habit. When going out of the house, you should keenly avoid places where indecent and immoral acts are carried out so as not to fuel jealousy in your husband’s heart.
Allaah knows best.