(for jailbroken devices). If you have a jailbroken iPhone 3G on iOS 4.2.1, you could theoretically install "AppSync Unified" and then use a cracked IPA. However, most cracked Messenger IPAs from that era were built for iOS 5+.
Most users did not download Messenger separately from the main Facebook app back in 2010. The standalone Messenger app was not popular/required until later. Consequently, the "last compatible version" for iOS 4.2.1 might not exist for the standalone Messenger app—it often only goes back to iOS 7. You will have better luck installing the main Facebook app using this method, which historically supported iOS 4.2.1 via legacy builds. facebook messenger ipa for ios 4.2.1 download