The wording here is a bit shall we say unhappy. As far as I understand it the classical Egyptian orthography proper—used for writing native Egyptian words—has indeed only consonants, something that Adolf Erman stressed in his 1894 Altägyptische Grammatik p7 (https://archive.org/details/agyptischegramma00erma/page/n31/...):

Unsere Umschreibung dieser Zeichen darf nur als 14 eine ungefähre Wiedergabe der betreffenden Laute gelten; sicher steht aber durch das Koptische (vgl. K§ 15) und durch die Art, wie semitische Worte im Ägyptischen, ägyptische im Semitischen wiedergegeben werden, daß sämtliche Zeichen Konsonanten darstellen. Die Vokale bleiben ebenso wie in den semitischen Schriften unbezeichnet. — Uber den ausnahmsweisen Gebrauch einiger Konsonanten zur Andeutung bestimmter vokalischer Endungen vgl. §§15— 16; 18; über das \\ i vgl. § 27.

Erman already hints at the extended usage of hieroglyphs that does include vowels, famously used for the names of Ptolemy and Cleopatra (not that Cleopatra, they all had the same name) on the Rosetta Stone, and also for the name Alexander. However, that usage is not as simple as "𓄿 = a, 𓇋 = i, 𓅱 and 𓏲 = u". That's also known as the "alphabet for tourists", and while not entirely wrong, it is more of a caricature than anything.

As for the reasons vowels are omitted I can only offer speculations. I'd like to offer the observation that all writing is difficult and rare in the history of mankind; we've only had writing for the past 5,000 years or so whereas how to make fire has been known for at least 50,000, maybe up to 500,000 years (according to latest findings in Great Britain, that we know of, legal restrictions apply, etc).

Second, all writing is defective as compared to speech. It may also add things that are not in speech (something that Japanese orthography is famous for), but there are always important aspects of speech that are lost in the written. The way writing works is not like, say, a phonograph that reproduces sound waves, it works more like a punched tape that reproduces patterns of symbols. From those patterns, the reader must reconstruct the spoken word, re-enact it in a way that only works by filling out the gaps—many gaps in all kinds of writing. Now, when we look at what aspects of speech get omitted in writing, it's the weakest parts: frequent victims are phrasal prosodies, for which we have a bare minimum of '?', ',', '.', '!' in Latin, all of which are post-classical era developments. We also have spaces between words, only used sparingly in antiquity, and regularly from the Middle Ages (10th c or so). All of these used to not be written and were left for the reader to reconstruct. Similarly in Literary Chinese. Speaking of Chinese, if there's any aspect that can most easily be left out, it's the tones in alphabetic writing, and in fact that's what Vietnamese speakers often do when in a pinch. BTW Vietnamese uses an alphabetic orthography but although there were trends to use hyphens to connect syllables, post-1975 orthography is written only with spaces between syllables, with no way to tell where words start and end (https://en.wikipedia.org/wiki/Vietnamese_punctuation#Modern_...), which is likewise left as an exercise to the reader.

So back to the question—why didn't the Ancient Egyptians write vowels? Well, they sometimes did, especially when writing loan words or foreign place names from some point onward (I guess late Middle, early New Kingdom, but not sure), but otherwise, they left out vowels as the 'weakest' part of spoken language, coming right after word separators, sentence markers, prosody—all of the aspects of spoken language that are underrepresented in all orthographies. This consonants-only or consonants-mainly approach is, of course, inherited by Arabic, Hebrew, Amharic, and Indian writing systems, all of which have consonants as their pivotal elements, with vowels taking a second, sometimes optional place.

Egyptian Hieroglyphs: Lesson 1