Why shouldn't Gentiles keep Shabbat?

I know little about Judaism and it's a first time question, so please forgive any mistakes.

According to this question non-Jews are forbidden from keeping Shabbat. What is the reasoning behind this? I would have expected keeping Shabbat to be a God-honouring thing, especially in the cited case of a person considering conversion.

Answer

This article brings several reasons why gentiles are forbidden from observing Shabbos:

1. The Rambam in codifiying this law (Melachim uMilchamot 10:9) explains that the issue is in gentiles innovating their own laws:

Similarly, a gentile who rests, even on a weekday, observing that day as a Sabbath, is obligated to die. Needless to say, he is obligated for that punishment if he creates a festival for himself. The general principle governing these matters is: They are not to be allowed to originate a new religion or create mitzvot for themselves based on their own decisions. They may either become righteous converts and accept all the mitzvot or retain their statutes without adding or detracting from them.

2. The Maharsha (Sanhedrin 58b) compares Shabbos to the bride of the Jewish people, and compares gentiles observing it to adultery:

The Maharsha explains that the Sabbath is, metaphorically, a bride. Indeed, the Talmud refers to the Sabbath as a bride and the Shabbos is greeted in the same way that a bride is greeted. This imagery was immortalized by Rabbi Shlomo Alkabetz (a 16th century poet and Kabbalist from Tzfas) in his classical liturgical song, Lecha Dodi, which is sung just before the reception of the Holy Shabbos. Rabbi Avraham Sperling writes, based on this allegorical comparison, that “Shabbos” is the female companion to the Israelite nation. The Jewish Nation is “married” to Shabbos. Therefore, when a non-Jew follows the rules of Shabbos, it is as if he is committing “adultery” with the married bride “Shabbos”, and so he is liable for the death penalty.

3. He suggest (based on Rashi's explanation) that the resting of Shabbos is an exclusive gift to the Jews:

When Adam sinned by eating the Forbidden Fruit, he was punished by all future males having to work, “with the sweat of his brow.” This implies that HaShem expects man to work continuously without rest. However, two thousand four hundred and forty-eight years later, HaShem granted the Jews a special present, namely, the Holy Sabbath, with which they can rest, in contrast to the remainder of society. Therefore, world society is not allowed to rest because of the curse of Adam, while the Jews are allowed to rest because the Torah specifically calls for a Mitzvah of Shabbos, which was a unique gift granted to the Jewish Nation . . Rabbi Meir ben Todros HaLevi Abulafia (1170-1244) explains that the gift of Shabbos was given specifically to the Jews, and therefore if a Noahide keeps Shabbos, he is actually stealing from the Jews and is therefore liable for the prohibition of stealing (which is one of the Seven Noachide Laws).