Why analysis stage of software engineering consider so important?

It is by far the most important stage. It is at that stage that it is established what the software is meant to do. If you don't know what the software is going to do, then you can't create it. If you don't get the details of what it is meant to do correct, then when the software is produced it may not do what the user wants. For big systems there is a lot of details to be established. An existing manual system may be being replaced by a software system. So it is important to understand to the finest detail what exactly happens in the manual system. That can take weeks, even months. All kinds of questions need to be asked and answered. The analysts need to know what happens at every stage of the process.

Later in the stages of software engineering the designers may still find they have to go back and get more details so that they know what is meant to happen in certain situations. Any mistakes that get into the system can cause a lot of problems later and are harder to fix and slower to fix. By asking the correct questions and getting the right information at the analysis stage, those subsequent delays can be avoided. So the analysis is critical to get correct.