That’s not true. Actually, it’s quite the opposite. To the best of my knowledge, the only Arab countries where a woman can pass on her citizenship to her children are Algeria, Egypt and I think very recently Jordan (although in the latter, it’s apparently very difficult in practice, and I believe there’s an exception made to exclude Jordanian women married to Palestinians). Here are a list of “reservations” made to the UN’s Convention on the Elimination of all forms of Discrimination Against Women (look for references to Article 9 paragraph 2, which gives women the right to give their nationality to their children).
Otherwise, Syrian women cannot give their citizenship to their children, nor can Palestinian women or those in the Gulf, the Maghreb (see update), etc. To the best of my knowledge, there is a loophole for children who are not recognized by their fathers. For more country-specific info, you can look here.
UPDATE: May in the comments points out that Tunisian women can also give their nationality to their children. However, when I looked up the official code in Tunisia, I found that it doesn’t apply to children born abroad, only in Tunisia. This reform dates back to 1993 according to Freedom House.