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Rava bar Rav Chanan refused to cut down his fig trees because Rav Chanina’s son died because he cut down a fig tree.
There is a prohibition from the Torah to cut down fruit bearing trees. It is not clear, however, that the prohibition should apply in this case. Tosfos asks a question from a Gemora in Bava Kamma (92a). The Gemora says that one is allowed to cut down a fig tree in order to save vines. Grapes are considered more valuable than figs and therefore it is not considered destructive to cut it down. Why then did Rava bar Rav Chanan refuse to cut down his fig tree?
Tosfos answers that one is only allowed to cut the fig tree if it is doing serious damage to the vines. In our case, the damage was not so severe so it was not permitted.
The Rosh in Bava Kamma permits the cutting of a fruit tree if one needs the space in which the tree is situated.
Based on this, the Taz (Yoreh Deah, 116) allowed someone to cut a fruit tree in order to build a house.
The Ya’avetz, however, requires that one have a gentile cut the tree based on a different understanding of our Gemora. The Ya’avetz is bothered by the question of Tosfos. If it is permitted to cut the tree, why was Rava bar Rav Chanan afraid of a curse? The Ya’avetz comes to the conclusion that even though it is permitted according to halachah, there is still a curse. Therefore one should never cut the tree down by himself, but rather have a gentile do it. Many people conduct themselves according to this opinion even though almost all the Rishonim don’t learn this way.