There are four keys one will have upon the creation of their account:

• Private Key - Used for Posting, Commenting, Resteeming, Follow/Unfollow
• Active Key - Same as Private Key + Transfers, Power Up & Down, Witness Voting
• Owner Key - Same as Private and Owner Key
• Memo Key - Only for viewing Private Memos

Now unto your question:

When you login via Steemit.com, it will only ask and accept "Posting Key" (or Master Key) which will only allow access to Posting, Commenting, Resteeming and Follow/Unfollow but not transferinf of funds. 

If you want to have access to wallet transfers, you need to use your "Active Key". Thus it seems that they kept on asking for passwords but what really happens is that they are only asking for the key for the corresponding action. These are all for the sake of security.