This is a question that creates suspicion in Outlook and Hotmail users, why Outlook / Hotmail asked me my phone number? Since years we are instilling that we never leave our phone number on any web.
Once you create a new account in Outlook or Hotmail (both platforms Microsoft), user has seven days to complete the security information or your account will be locked, but need not necessarily leave our phone number, we can also leave an account alternate email.
Other platforms free email like Yahoo Mail or Gmail also ask us and our cell number for the same reasons of safety the same way as Facebook and Twitter, although the latter is still under implementation period.
Using our phone number is to recover our account in case you forget the password or being the victim of some form of impersonation, Microsoft offers guidance for account recovery blocked in Outlook you can see in the following link.
But to answer the eternal question of leaving or not my phone number on a web standard answer is yes but with some caution, since none of the major web platforms such as Outlook, Google, Facebook or Twitter will fraudulent use our phone number, but we have to be very careful with platforms where services are billed through "sms premium", but again the confidence that we provide the major planks of the Network.