Shalom and thank you for your question!
There are many aspects to this question. Firstly, what is a sin? The joke goes that a Jew answers a question with a question… What is a Mitzvah (translated as good deed but meaning much more than that)?
What is the obligation of a Jew to his/her Creator?
The Sages of the Talmud teach us that G-d created the ‘blueprint’ for the world and then created the world. This blueprint is the Torah, which contains 613 commandments for Jews, and seven ‘Noahide laws’ for non-Jews, which include things like setting up courts of justice, not committing idolatry or adultery and more.
Tbe 613 commandments for the Jews are based on wording in the Five Books of Moses, including the Ten Commandments. Not eating meat and milk together constitutes certain of the 613 commandments. (in other words more than one of the 613.) Various great scholars such as Maimonides listed those commandments and what are the sources for them in the Torah.
The Talmud is the basis for the code of Jewish law, and more and more books of Jewish law come out every year as the world changes and there is a need to understand how to apply the principles of Torah knowledge to current circumstances. The principles do not change. Torah scholars process the information according to the principles handed down through the generations.

One of the Hebrew words for sin is Aveirah. It comes from the root ‘avor’, which means cross over. In other words, a sin means crossing a boundary, a red line if you will. Mitzvah comes from the root ‘Tzavta’, which means connection. In other words, when you fulfill a Mitzvah, a Torah precept, you are connecting with G-d, even though you are not physically aware of it. In the Tanya, the basic text of Chabad Chassidic teaching, it is explained that there is a phrase in the Torah, ‘Yaakov chevel nachalato’, meaning Jacob is a rope to his heritage.
This teaches us that our relationship with G-d is akin to a rope made of 613 strands. When we disobey a command, one of the strands is torn. When we rectify something we did wrong, we ‘retie’ strands, and then the rope is stronger than before!
We are grateful to G-d for creating us and giving us the mission of fulfilling the Torah, which ultimately will bring about the complete Redemption, when there will be complete peace and prosperity, and G-d will ‘remove the spirit of impurity from the earth’.
We hope this helps, feel free to ask more…
All the best!
Additionally, I would like to point out that although we obey the commandments unquestioningly due to their Divine origin, knowing that G-d’s wisdom is infinite, nevertheless there are opinions among the commentaries that connect consumption of milk and meat (or poultry) with being cruel, because there were times when a goat would give birth to a couple of kids, and while one kid was slaughtered for food, the mother goat had an abundance of milk, so people indeed took the extra milk and cooked the kid in it. The Sages teach us that keeping the commandment of not eating milk and meat together helps us stay away from behavior like that, which can make us insensitive, and can also lead to being gluttonous.
Again, the Torah outlook is that we obey the commandments to connect to G-d’s will, which is enclothed in the commandments, and not because we understand the Divine wisdom, but we do try to understand what it teaches us.