The r sound I can create (a) without moving my tongue (after it is put into place), and (b), without closing the mouth cavity entirely. Like rrrr.... To me then it seems like a vowel.
For h, it is basically an unvoiced vowel.
For w, it made by rounding my lips, like one. In that sense it seems like a vowel.
Wondering why they are considered consonants instead.
The International Phonetic Alphabet draws a very arbitrary distinction between consonants and vowels, and categorizes them completely separately. But in truth, there's not any major phonetic difference between [w] and [u].
In actuality, the main difference between /u/ and /w/ is /u/ is the nucleus of a syllable, /w/ isn't. In other words, every syllable is a "vowel" in the middle, potentially with some "consonants" on either side, and this is the only thing that reliably distinguishes them.
This feature is called syllabicity, as in, "vowels" are syllabic, "consonants" aren't. Many languages have both a syllabic and a non-syllabic version of the same sound: if you speak General American English, you have six such pairs, m n r l j w.
The IPA encodes five of these pairs with separate letters: j~i w~u ʕ~ɑ ɰ~ɯ ɥ~y. For all the rest, you can mark the consonant with a line (m̩) or mark the vowel with a curve (e̯) to switch its syllabicity on or off.
The letters [r,w,h] conventionally refer to "consonants", specifically, non-syllabic segments, whereas [r̩,u] refer to syllabic segments ("vowels"). Similarly, [j] is a consonant, [i] is a vowel – but [j,i] are the same except for that difference (and also, [m,n] are non-syllabic, [m̩,n̩] are syllabic). [h] is a bit of a problem because it has no unique syllabic variant that can be articulated on its own, nut in a sequence like [ha, hi], [h] is phonetically a voiceless version of the following sonorant segment, so you could transcribe "ha" as [ḁa], "hi" as [j̥i].
The terms "consonants" and "vowel" are confusing since they are used in multiple ways. Sometimes, "consonant" vs "vowel" refers to syllable structure pattern, in which case [h,r,j,s,l,p...] are "consonants" and [a,r̩,i,l̩] are "vowels" (usually nobody calls [l̩] a vowel but [r̩] is often called a vowel, in English). But if you are talking about the decree of constriction in a sound, then the terminology changes. This is recognized in some theories of phonological features sucha s the SPE theory, where "consonantal" refers to a particular degree of constriction and "syllabic" refers to syllable-structure function. So [h,j,w] are non-consonantal, but non-syllabic; [a,i,u] are non-consonantal and syllabic; [m,l,p,s] are consonantal and non-syllabic; finally, [m̩,n̩,l̩] are sonsonantal and syllabic. The standard definition of "consonantal" is "a segment with more mid-sagittal constriction that that of [j]".
Versions of r add one other complication. American English r is generally an approximant [ɹ] and not [r], and it is non-consonantal which can be syllabic or not. In other languages like Serbian, Croatian and Sanskrit, there is a syllabic version of [r], thus [r̩].
