The reason may vary as each user has his own unique software/hardware configurations.
Additionally, Steam will occasionally verify all of its files, to ensure that everything is as it should be. This window is displayed while the update is installed or verification process is running to provide feedback to you (the user) that something is actually happening, rather than staying completely silent, leading you to think that the application hasn't started.
Windows Firewall sometimes marks some of these processes as malicious and tends to block Steam.
There may even be a conflict going where the Firewall is blocking Steam’s actions in the background.
If you are a member of the Steam beta program, it might be worthwhile opting out of the beta program and reverting to a previous version of Steam (it should do this automatically) to see if this resolves your problem.
Another thing that is mentioned in the Steam forums, is allowing Steam to verify all of its files and then closing Steam properly (rather than letting Windows kill it as it shuts down).