: Why do certain chords "lead" to another? I'm currently reading The Complete Idiot's Guide to Music Composition by Michael Miller and in the "Composing With Chords" section, a reference chart for chord leading was provided

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Your question can’t be answered without referring to the tension of the lead tones. The tones of a scale near the consonant intervals referred to the root have a tendency to lead to the next perfect interval. (Ti is tending to resolve into do, re to do, la to so, fi as augmented 4th toward so.) A similar tension show the steps near the 3rd and the 6th. (Fa leads to mi) The tension for a solution of a halftone step is stronger the the tension of whole tone.
That means that the altered tones have a stronger tendency to resolve into the next consonant interval (ri will lead to mi, si to la, ta to la).

These are just examples, you’ll find others by yourself.

According to Ernst Kurth (1913, 119–736) the major and minor thirds contain "latent" tendencies towards the perfect fourth and whole tone, respectively, and thus establish tonality. However, Carl Dahlhaus (1990, 44–47) contests Kurth's position, holding that this drive is in fact created through or with harmonic function, a root progression in another voice by a whole-tone or fifth, or melodically (monophonically) by the context of the scale. For example, the leading tone of alternating C chord and F minor chords is either the note E leading to F (if F is tonic), or A? leading to G (if C is tonic).

The leading-function of a chord and its tendency to resolve into another chord is a similar function as the function of the leading-tones it is consisting of.

In the link below is explained how this tension of the leading-tones as an element of chords are functioning.

The rest is up to developing as you surely are not what the title of your book says.
en.wikipedia.org/wiki/Leading-tone
and here is just another link explaining the doremi as relative scale that can be transferred to all scales and keys:

Movable do solfège

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Is there a scientific or logical explanation to why these chords
"lead" to the specified chords,

Albrecht already answered as to the musical logic regarding 'leading.' Basically, half steps have a strong pull.

But I think something should be said about 'common patterns.'

or is it simply just a result of common patterns in popular music?

Yes, common patterns are important. In fact I think several of the options for progressions in the chart come from common patterns. But the chart doesn't explain the connection to such patterns.

This the following is a loosely organized list of some patterns you might look into:

'functional harmony' which groups chords in predominant, dominant, and tonic categories and defines a syntax of progressions from predominant to dominant to tonic.
'strong progressions' generally considered root movement by descending fifth, descending third (from the tonic), or ascending step (from IV to V)
hugely important are 'harmonic sequences' where typically a two chord progression like a descending fifth or fourth is then repeated a step higher or lower, one very well known sequence is the circle of fifths.
root progression by step is also used, but in classical style the chords will be in first inversion some refer to this as 'fauxbourdon', root position chords can also move by step but it is probably more common with pop styles bVI bVII i is one example.

That isn't a complete list of patterns. It's just a starting point. But even from that short list certain things can be seen.

For example, iii ii is considered a weak progression compared to a strong progression like roots by descending fifths. But, in the context of root movement by step it's a fairly common pattern.

Of course we need more than two chords to establish a clear pattern.

And that is what I think the potential pitfall of the chart is. It doesn't explain how some of those potential progressions fit into common patterns.

Nearly any two chords could could be used in succession depending on the surrounding musical context. In that sense the chart is both obvious and meaningless, because it doesn't explain how to create the context that gives chord progressions meaning. It's a kind of musical anti-pattern!

Some might say the chart is a kind of 'harmonic training wheels' for a beginner, but I actually think it will just lead to a beginner becoming confused.

Without some knowledge of common patterns there is the risk of the chart producing weak, meandering progressions like... I ii viio iii ii IV iii ii.