When a company wants to redesign their web site in most cases it means they want to improve the User Interface and User Experience.
It is incorrect to assume that everything about the old design is wrong. Existing users become custom to the old interface and by changing everything in the redesign, you might lose the positives the user really likes.
Before redesigning a website, you must always conduct research on your current website to identify the positive features.
A negative example is online banking from Barclays. Every time I get used to their new User Interface, they change it in such a drastic way, which may be an improvement but very confusing as the changes happen far too frequently.
On the other hand, a positive example is how Amazon hardly changed their interface and user experience how to search and purchase a product. The main interface was designed correctly the first time around and any further changed are so minor you hardly recognise them but they work out as an improvement.
When drastically changing the new User Interface and assuming that it is the best way to go forward without considering the positives from the old web site you might drive your users away to competitors.
As they say... "Don't fix it, if it's not broken" should always be in the back of your mind when starting a redesign. Most companies do not even know what is wrong with their website and start redesigning without knowing what is broken.
Of course, you cannot keep everybody happy but it is essential to research user's behaviour and test new concepts with them to ensure the redesign has been done correctly.
A redesign should never been done because it needs a new look. It should be done if in certain areas on the website the User interface has bad usability, which needs to be improved.Bottom line is that when redesigning a website you should always research certain features in the existing website, which the end user is comfortable with and really likes. Therefore, these features do not have to be changed but implemented in the new User interface design. If you start redesigning without considering your end users and not researching the old website, they start to complain or lose them.