It might seem old fashioned, but it's important to hold on to traditions, no matter how much the pressure of modern life might push against it. Closing offices on Mother's Day is a relatively small thing that provides a morale boost for many people - something Mexico, like many countries, is badly in need of at the moment.
Mother's work long enough hours just being mothers, so it makes sense to give a day a year where mothers can enjoy some needed respite and down time. In Mexico the tradition of closing government offices for Mother's Day should endure and continue to give thanks to all the mothers out there.
This practice shows mothers a great deal of respect. There are undoubtedly mothers, sons and daughters working in these government offices who otherwise would not be able to celebrate the holiday. Closing government offices sets an example for people all over the country and sends the message that mothers should be revered and celebrated.
A government should reflect its citizens' values and respect the traditions of its prevailing culture. Mothers, and the attachment to one's mother, are very significant in Mexican culture. Mother's Day is always celebrated on May 10, so the day may not always be a Sunday. There can be some extra inconvenience when government offices are closed on a weekday. But the day is a popular as a day of celebration, and private businesses like restaurants and florists benefit from extra business on that day, in part because people are off work and free to focus on honoring mothers.