One of the main themes of Peisach is liberty. Another theme is unity. It is explained that we say "dayeinu" to being brought to Har Sinai, because on that day, klal Yisroel experienced unity. It also says that the whole reason for the slavery in Egypt was bittul: to mevatel our egos, making it possible for each of us to accept each other else.
What's the value of unity, and what is its connection to liberty?
First, there is a concept in Chassidus that lower unity parallels the upper unity. In some discussions, it is stated that lower unity results in upper unity.
"Lower unity" can refer to Malchus and z"a, or the lower spiritual worlds, but it can also refer to us: the Jews. This point of view is stressed in the ma'amor of Derech Mitzvosecho in which Tzemach Tzedek talks about Ahavas Yisroel. He states that one must unite in his soul all the sparks of all the Jews (represented there) before he can offer his soul as a karbon during davening. With a blemish within a Jew, he cannot pray effectively.
But, from the positive perspective, the reason to create a lower unity is that it results in upper unity: within the name of M"A. That is because all neshamos are routed in the Above, and when one creates unity between them (or between sparks representing them), one also creates a unity within their source. This is why it says that all of Torah is about the mitzva of Ahavas Yisroel. The purpose of all of Torah is to create unity Above through performance of the mitzvos Below. This is the effect that mitzva of Ahavas Yisroel accomplishes.
A philosophical, rather than mystical, explanation is found in the Duties of the Heart by R. Bahye. He says that the purpose with which G-d made all the multiple forms of creation is to show His lack of limitation: that anything can be created by G-d. Demonstration of G-d's unity is another purpose: we can see how all the creation works together as a machinery, each part complimenting each other, all bound by the same laws.
From another perspective, it is why, as mentioned above, we are given mitzvos: we have to demonstrate the unity of purpose and function Below. It is obvious Above that G-d is one. This is simply because He is singular and indivisible. He is one entity with no limitations or parts. But, it is also true, as R. Bahye mentions, that G-d has potentials to create many forms of existence. Perhaps there is a disunity in these potentials? What does G-d's potential to create a tomato have to do with G-d's potential to create a banana? They are separate, independent potentials, one might say, and they do not unite with each other except in the fact that they derive from the same Creator.
So, if we demonstrate that in fact both the banana and the tomato have the same purpose, and their existence Below can be used to demonstrate the existence of the Creator Above by carrying out His Will with them, we make a chiddush: we demonstrate unity even in the yechoilos, the potentials of G-d.
So, for all of the above reasons, unity is crucial.
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What does it have to do with liberty? Because liberty makes unity possible. The concept of liberty is lack of oppression. When a person is free, he is free to be himself. If I force everyone to wear what I like to wear, I am forcing them to be me. If I let everyone wear whatever they want to wear, I am letting each person be himself.
So, one key to liberty is respect. And respect is all about boundaries. Paradoxically, because of the nature of people to express their will (given the opportunity), it is the fact that the stricter the boundaries around each person and the more respect the others have for those boundaries, the closer people can be to each other.
To explain: every person has his own desires and character. Every person tends to express them. If others contradict this expression, he tends to move away to find a space where he can do so. (Or he is forced to stop being himself and conform to others' will.) This is why there have been massive emigrations throughout history: people want to go somewhere where they can live their lives the way they want to live them. (Of course, another reason is that people go towards the places where life is already better. But, for many people, part of life being better is lack of oppression. Another point, already made by me earlier, is that freedom and prosperity correlate strongly throughout the history.)
So, paradoxically, if I create a very strong boundary around some person, a boundary that I cannot cross, I can coexist with that person — as close as that boundary. But if there are no boundaries around that person that I respect, than the person will tend to move away from me, and no co-existence will be possible.
There are many nuances here that I am not developing fully. Obviously, one person's boundaries cannot overlap with another person's boundaries. We might respect someone's right to wear whatever he wants, but not his right to beat his children to a pulp. Or his right to drill a hole under himself in a shared boat. Because those "boundaries" include other people — and their boundaries — in them. What exactly the picture of the co-existing boundaries should look like is a separate question.
Let us assume for now, therefore, that I am talking about legitimate boundaries. What hat someone wears. Whether he keeps gebrochts or not. Which Rebbe he follows. Whether he follows strict diet or whether he eats whatever he wants (within boundaries of kashrus). These are legitimate choices that one can make, and we have a choice: to respect other people's choices — and therefore co-exist with them in unity — or to disrespect them and push them away from us, creating disunity.
So, this is one connection between unity and liberty that I see. If you give Chessed liberty to be Chessed and give Gevurah liberty to be Gevurah, they can coexist with each other in unity.
The fact that we were liberated only to serve Hashem doesn't change the equation. Every person has his own circumstances and his own place in creation (both space and time), and that person and his place are dear to Hashem. We must love and respect our fellow Yidden and allow them to fulfill the role for which they were liberated by granting them freedom within their individual circumstances and characters.