Because your Bank has not made their website Safari compatible.
Some banks are notoriously uncaring and lazy about what systems and browsers they support.
As it says in this document:
"Safari complies with standards, but not all browsers do. This article explains how to design, modify and validate your website so that it can be rendered and read properly by all major browsers."
Try this: after you have logged into your bank's page, open another tab or window with http://validator.w3.org/ and paste in the URL of your bank's page, which will reveal any noncompliance with standards.
The bank/s need to read this:
"Safari is one of the most standards-compliant browsers ever built. Thus, your best bet for ensuring your pages render properly in Safari — today’s version and beyond — is to follow web standards. For a great overview of web standards, check out Mozilla.org’s article Using Web Standards in Your Web Pages."