Question

why do some atoms form positive ions and others form negative ions?

Answer 1

because some atoms prefer to loose electron or gain electron to become noble

Answer 2

all atom want to make their electronic configuration like that of noble gases thus some loose electron
for example Na has 1 electron in it's last shell, isn't it better to loose that one electron rather then to gain 7 more electrons to have same electronic configuration as that of one of noble gases? that's why by loosing that electron it becomes positive ion
some gain electron
for example Cl has 7 electrons in its last shell, isn't better if it gains 1 electron rather then loosing 7 electrons to have same electronic configuration as that of one of noble gases? that's why it'd gain 1 electron and become negative ion