This is to supplement Sree Charan's correct answer with quotes from Shastras.
The Manu Smriti says that there is no Vedic sacrament for women.But what is Vedic sacrament for men the nuptial (wedding) ceremony is that for the women.
Hence, removing the mangal sutra (which is considered as a proof or symbol of the marriage) by women, is considered as offensive as Dwija men removing their Yajnopavitas (the sacred threads).
Manu smriti 2.67.Vaivahiko Vidih Streenam Sanskaroh Smritah|Patiseva Gurou Vaso Grihartho Agni Parikriya|| The nuptial ceremony is stated to be the Vedic
sacrament for women (and to be equal to the initiation), serving the
husband (equivalent to) the residence in (the house of the) teacher,
and the household duties (the same) as the (daily) worship of the
Update regarding the importance of wearing Mangala Sutra:
The fifth step in a Vedic marriage is Maangalaya Dhaaranam.
There is no Veda Mantram for tying the mangala sutram (auspicious
thread) around the neck of the bride by the groom. The latter takes
the mangala sutram in his hands and recites the following verse:
mângalyaṁ tantunânena mama jîvanahetunâ | kaṇṭheḥ badhnami subhage!
sañjîva śaradaḥ śatam || This is a sacred thread. This is essential
for my long life. I tie this around your neck, O maiden having many
auspicious attributes! May you live happily for a hundred years (with