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This rule has very archaic origins. When listening to a monk explaining the dhamma we normally put the monk in a more respected position (e.g. sitting in a chair while we sit on the floor); when we do this we tend to treat the monk's words as more important so being humble is helping us to learn the dhamma.
At the time of the Buddha sunshades and umbrellas were a sign of luxury. At that time if someone used a sunshade while the monk didn't have one then it is as if they see themselves as more important than the monk and they are less inclined to care about the monk's words.
Thanissaro Bhikkhu's book The Buddhist Monastic Code I has some explaination about this rule
SN 6.2 records that the Buddha himself had the highest respect for the Dhamma he had discovered; that, as others might live under the guidance of a teacher, honoring and revering him, the Buddha lived under, honored, and revered the Dhamma. He enjoined his followers to show the same respect for the Dhamma not only when listening to it but also when teaching it, by refusing to teach it to a person who shows disrespect. The following set of rules deals with situations in which a listener, in terms of the etiquette at that time, would be regarded as showing disrespect for a teacher or his teaching. As the Vinaya-mukha notes, a few of these cases—such as those concerning footwear—are not considered disrespectful under certain circumstances at present, although here the exceptions given for listeners who are ill might be stretched to cover any situation where the listener would feel inconvenienced or awkward if asked to comply with the etiquette of the Buddha’s time. On the other hand, there are many ways of showing disrespect at present that are not covered by these rules, and an argument could be made, reasoning from the Great Standards, that a bhikkhu should not teach Dhamma to a person who showed disrespect in any way. Dhamma here is defined as any statement spoken by the Buddha, his disciples, seers, or devat›s, connected with the teaching or with its goal. See Pc 7 for a more detailed discussion of this point.