I'm a BA with over twenty years experience working within the financial services and legal industries. In addition to being a Certified Scrum Master since 2009 I have membership of the IIBA, associate membership of the BCS and membership of the British Standards Society. I have been keen wherever possible to use the Scrum approach for developing software solutions for employers and clients. Scrum and business analysis are not incompatible, thinking they are demonstrates to me a lack of understanding of one or both.
Scrum is there to deliver business critical working software as quickly as possible.
Business analysis is about understanding the strategy of a business and being able to say this is the current state, here's the future state and this is what is required to get there; the required to get there could involve a software development angle and that is where Scrum becomes a very powerful tool.