How and why do we need to adjust self-employed income? Could you please elaborate?

There are two reasons.  

1) specific, very uncommon situations. Such as clergy and another situation I can think of is notary income or state grants for certain industry specific projects, which are taxable for federal. But, that's why I say, people nearly always know that they are in a 'different' situation that requires adjustment. There isn't actually any reason that normal self-employment income would be adjusted, so I wouldn't worry that you are missing out on anything - I know this line may make you feel that way! - it's deceiving.  

2) The most common reason this line might be used, is if you are a part-year resident and are filing in multiple states, with some income not earned in the state, or as a non-resident reporting income earned in the state. As a resident all earnings are reported.

Thanks a lot for your detailed response 🙂
It helps a lot.

As self employed I used short SE form. That form is no longer. Why do now I have to use farm/non farm optional methods to move on from line 4 on the SE form. Never had to before.

Must I use any of these methods now?