Resemblance with alkali metals:

1. Like alkali metals, hydrogen contains one valence electron in its valency shell. 

$H : 1s^1$
$Li : ( He ) 2s^1$
$Na : ( Ne ) 3s^1$

Hence, it can lose one electron to form a unipositive ion.

2. Like alkali metals, hydrogen combines with electronegative elements to form oxides, halides, and sulphides.

Resemblance with halogens:

1. Both hydrogen and halogens require one electron to complete their octets.

$H : 1s^1$
$F : 1s^2 2s^2 2p^5$
$Cl : 1s^2 2s^2 2p^6 3s^2 3p^5$

Hence, hydrogen can gain one electron to form a uninegative ion.

2. Like halogens, it forms a diatomic molecule and several covalent compounds. Though hydrogen shows some similarity with both alkali metals and halogens, it differs from them on some grounds. Unlike alkali metals, hydrogen does not possess metallic characteristics.On the other hand, it possesses a high ionization enthalpy. Also, it is less reactive than halogens.

Owing to these reasons, hydrogen cannot be placed with alkali metals (group I) or with halogens (group VII). In addition, it was also established that H$*$ ions cannot exist freely as they are extremely small. H$*$ ions are always associated with other atoms or molecules.
Hence, hydrogen is best placed separately in the periodic table.