The misconception that women are deficient in intellect has arisen because of a wrong translation of the Arabic phrase Nāqiṣatu al-‘aql wa al-dīn of the hadith you have quoted.
The word ‘Naqṣ’ has generally been translated as ‘defective’ keeping in view the Urdu meaning of the word. However, in Arabic, the verb ‘نَقَصَ’ (Naqaṣa) means ‘to reduce’ and the word ‘عقل’ (‘Aql) here means ‘worldly affairs’ since it has been used in conjugation with the word ‘دين’ (religion). Keeping in view, both these aspects, the correct translation of the above phrase, if the context is also taken into consideration, is that women have been given a relief and reduction in their worldly and religious affairs.
The relief in worldly responsibilities, as is mentioned in this Hadith, is that women have not been dragged in certain activities and spheres. For example, the Qur’an urges men to testify on legal documents so that women are relieved of appearing in courts and wasting their precious time on affairs which others can handle. Only if men are not available should a society involve women in such affairs.
The relief women have been given in religious affairs is that they are not required to pray or fast during their monthly periods as is mentioned in this Hadith.
So what must be kept in mind is the fact that the meaning of a word does not always remain the same in two different languages. For example, the word ‘غَلِيْظ’ in Arabic means ‘firm’ while in Urdu it means ‘dirty’. Thus the Qur’an (4:21) has referred to marriage as ‘مِيثَاقاً غَلِيْظَا’ (a firm agreement).
Moreover, people who think that women are less sensible than men on the basis of this Hadith do not realize that the Hadith is not merely saying that women are nāqiṣatu al-‘aql, it is also saying they are nāqiṣatu al-dīn. If nāqiṣatu al-‘aql means that there is some defect in their ‘aql (intellect), then by the same token, nāqiṣatu al-dīn should mean that there is also some shortcoming in the religion they follow! This of course is absurd and as referred to above is the result of keeping the Urdu meaning of the word in consideration.