Q.Why the elements belonging to the same group do have similar chemical properties?

Step 1. Recall section 7.3.2. A new (larger) shell is added at each step down a group, but for groups 1, 2 and 13-18 the GENERAL outer electronic configuration stays exactly the same down the whole group (e.g. group 1 is always $ns^1$; group 17 is always $ns^2np^5$).

Step 2. Connect configuration to chemical behaviour. Chemical properties — how many bonds an atom forms, whether it tends to lose or gain electrons, its typical valency and oxidation states — are governed primarily by the number and arrangement of VALENCE (outer-shell) electrons, since these are the electrons directly involved in bond formation. …

Connecting the down-group constancy of outer electronic configuration (section 7. …

• Saying properties are 'identical' down a group rather than merely SIMILAR — magnitude (reactivity, radius, etc.) still varies down the group even though the general TYPE of chemical behaviour stays similar. …