He is right that there are restrictions, needing your husband's permission is a restriction, but that is different from a ban.
I guess like most he buys into the propaganda that mohamidians are against abortion when that is not quite the case. There is a wide range of teaching from totally unacceptable (very rare) to partial birth abortions being perfectly ok (more places then you think). Mostly it hits at before twenty weeks and with the father's permission. Or even at the father's insistence.
It is sad how many people do not bother to do a simple search to find out if something is accurate or not before reacting.
http://www.hdip.org/public%20health%20law%20English.pdf
Palestinian Legislative Council
Public Health Law
Translated in to English by
WHO Office
For West Bank and Gaza
At pp. 5-6:
Article Eight1. it is forbidden to abort any pregnant woman by any means, unless there was an urgent reason to save her life and under the condition of having two specialized physicians as witnesses, one of them is a gynecologist and the following should be available:
a) a written approval from the pregnant woman. In the case of her disability to do so, the written approval should be obtained from her husband or her legal guardian
b) the process of abortion should be performed in a medical institution
2. the medical institution where the abortion took place should keep a record of the pregnant woman’s name, the date when the operation took place, the operation’s type, and justifications. This data should be kept in addition to the testimony of the two doctors and the written approval for the period of ten years at least.
At page 23:
Issued in Gaza City on the 27th of December 2004
15th of Zou El Ki’da 1425 Hegira
Rawhi Fatouh
President of the Palestinian National Authority