The reverse step
The retrosynthetic arrow (⇒) means “can be made from”. It is not a reaction: it is the reverse step of a known reaction, and it is only valid if that reaction exists and works in the presence of the other groups in the molecule.

The first step of the retrosynthesis of ibuprofen converts the acid into a nitrile. It is a functional group interconversion that does not change the skeleton but opens up a new disconnection: the C–CN bond is formed by nucleophilic substitution of cyanide on a halide, a reaction with no direct counterpart for COOH. Each reverse step is thus chosen with the next one in mind.
Writing reliable reverse steps requires mastery of the reactions of basic organic chemistry and of the conditions under which they occur. Review the preparation of acids by hydrolysis of nitriles and the preparation of nitriles in Organic Chemistry made transparent. A reverse step corresponding to an impossible reaction (for example an SN2 on a carbon of an aromatic ring) invalidates the whole route.