The reason other festivals got fixed to the Julian (and later Gregorian) calendar, while Easter (and hence Good Friday) is lunar, is partly (1) other festivals are much less theologically important, so they never needed to be treated as special cases; and partly (2) Easter started off being directly related to the Jewish calendar, both in terms of days of the Jewish week (Friday and Sunday) and in the setting of Jesus' death at the time of the Jewish Passover festival. And until the 3rd century, the Jewish calendar was lunar.

The formula for the date of Easter is a compromise, partly based on the lunar calendar, but also engineered to make sure Good Friday and Easter fall on the desired days of the week. As a result it doesn't always coincide with Passover.

The question of whether to pin Easter to the date of Passover in the Jewish calendar was a major dispute in the 2nd to the 4th centuries. The movement for pinning it to Passover originated in the Anatolian church, and is known as Quartodecimanism, from the Latin quartodecimus 'fourteenth', since Passover is pinned to the 14th day of the month of Nisan. At that time, in the mid-2nd century, the Roman church took the opposing position, that Jesus' death and (supposed) resurrection should be pinned to Friday and Sunday respectively. In the initial dispute in the 150s, Polycarp and Pope Anicetus simply agreed to disagree, but later generations couldn't handle the idea of different people doing things differently, so it got heated in the 190s, and never really went away until the Council of Nicaea in 325. In the end Quartodecimanism came to be regarded as outright heresy.

Lots of numerological and chronographical symbolism got involved in the dispute, and that's really what's responsible for the seasonal symbolism of Easter and Christmas: with Christmas pinned to the (traditional) date of the winter solstice in the Julian calendar, while Easter was kinda-but-not-completely linked to the spring equinox. Sometimes the symbolism got pretty wild. Here's part of a tract dating to 243, the De pascha computus ('computations about Easter'), sections 19-20:

He is the Lord in whose likeness the sun each year consumes 365 days and a quarter of a day; and that quarter day has three hours; and the three hours carry the likeness of the three days at the beginning of time when there was no sun or moon. And just as the three hours calculated four times over a four-year period make a day of 12 hours, so also those three days, persisting through four periods of three months each, indicated a year completed after 12 months. And so through this multiform trinity the 12 hours themselves indicate one gospel divided into four parts; and three months through four periods, that is, through the four evangelists, appear as the 12 apostles chosen for us by Christ.

These are the apostles by whose speeches we are instructed, and so we recognise that our Lord suffered in the 16th year of the reign of Tiberius Caesar, when he himself was 31. Now, to the 16th year and the 31, let us add 18 in the name of Jesus himself, and the resulting figure is 65. This is 300 short of filling the length of a year according to the course of the sun. And among the Greeks 300 is written with one letter, called tau, and tau plainly indicates to everyone the sign of the cross. So again let us truly believe that on 28 March Christ was born in the flesh; and that is the day the sun was created, as we showed.

(This is total pants-on-head crazy talk, so in charity I should mention that this is a very extreme case.)

Anyway, 28 March is three days after the traditional Julian date of the equinox (25 March), so the author of the tract is pinning the creation of the cosmos to 25 March, and the creation of the sun on the fourth day of creation. The author regards Jesus and the sun as symbols of one another, so they link Jesus' birth and death to the equinox too.

The reason for wanting to link Jesus to the equinox is partly because that's the time of year that Passover happens, but also because of a passage in the Hebrew Bible that Christians interpreted as referring to the Messiah, in Malachi 4.2 --

But for you who revere my name the sun of righteousness shall rise, with healing in its wings.

(I should parenthetically point out that this Christian interest in sun symbolism is decades earlier than the emperor Aurelian taking an interest in the worship of the Roman god Sol.)

The numerological thinking of the time took it that some major Hebrew prophets were born and died on the same calendar day, and this applied to Jesus, too; one sect, the Valentinians, thought his ministry lasted exactly one year (one month for each apostle). But in addition to that, early Christians were very interested in Jesus' conception, and by around the year 200 they were distinguishing his birth date from his genesis, which got reinterpreted as his conception date. It seems -- this can't be definitely proved, but Thomas C. Schmidt makes a strong case for it in this 2015 article -- that the end result was that Jesus was envisaged as dying on the same day he was conceived, rather than the same day he was born, and that put his birthday exactly nine months later on the winter solstice.

But like I said at the start, Christmas wasn't as theologically important as Easter, and his birth wasn't connected to Passover or days of the week in the gospels. So there was no pressure to have Christmas move around the way there was with Easter.

The pressure to pinpoint exact dates appears to be a direct result of the Quartodeciman dispute. The first exact dates that we see for Jesus' birth and death appear in Clement of Alexandria, just a handful of years after synods were convened around the Mediterranean to discuss the Quartodeciman dispute. By contrast, 1st and 2nd century sources are extremely vague about Jesus' birth and death day: the Valentinians regarded Jesus' ministry as lasting exactly one year, as I mentioned, but even they don't seem to have settled on specific calendar dates. Other extant sources -- Josephus, Tacitus, Justin Martyr, and Irenaeus -- put the start of Jesus' ministry in the reign of the emperor Tiberius, but offer no information beyond that. The heated debate over Quartodecimanism in the 190s seems to be the turning point where that situation changed: 3rd century Christians got extremely interested in chronography (e.g. Julius Africanus) and the conversion between lunar and solar calendars (e.g. Hippolytus of Rome, Anatolius).

Here's a four-part series that I wrote offsite last year, which delves into the development of dates for Jesus' birth and death over the first four centuries.