Out of all the nissim (miracles) that HaShem did for Klal Yisrael (the Mann, Makkos, Bar Miriam, etc) why was it specifically by this miracle that Klal Yisrael sang Shira?
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The Lubavitcher Rebbe (Likkutey Sichos vol. 23 pg. 153) asks what is unique about the two miracles of the splitting of the sea and the miracle of Nachal Arnon that we find specifically on these two occasions the Jewish people sang Shira.
He explains that these miracles were unique in that not only did Hashem help them, but they did not have to do anything at all. At Kriyas Yam Suf, Hashem told them, "Hashem will fight for you, and you shall be quiet". Similarly by Nachal Arnon, only after the people safely passed through the mountains they noticed the corpses of the Amorites who had attempted to ambush them (see Rashi to Bamidbar 21:14-16). This is in contrast to the other miracles Hashem performed for the Jews, in which they although the Jews received Divine assistance, they still had to fight themselves.
This is my own reasoning; I don't have a source.
Israel of course experienced other miracles before the yam suf, but until then they were still under Paro's control. They were not completely free to serve God and, ultimately, enter the covenant at Sinai. They could certainly have praised God for the earlier miracles (and maybe they did for all we know), but this one marked a transition -- they were really free now to say zeh eili and all that implies.
That seems worth celebrating to me!