Why do aromatic hydrogen atoms have a higher chemical shift value compared to aliphatic hydrogen atoms?
The chemical shift gives you information about how well shielded the nuclei are from the magnetic field. A proton at higher chemical shift values is deshielded, so the aromatic protons are obviously less shielded than aliphatic protons.

One effect that causes deshielding is the presense of electronegative atoms that draw electrons away from other atoms and thereby deshield them. But that is not the cause of the aromatic chemical shift.

The reason for that one is the ring current that is induced in a magnetic field. The induced current creates a local magnetic field that has the same direction as the external field outside the aromatic ring where the attached protons are, leading to the deshielding of the nuclei.