Question: Should only monastics teach the Dharma?
Answer: From the book ‘The Buddha and His Disciples’ by Venerable S. Dhammika is a section that can answer this question – ‘It is often mistakenly thought that it is the job of monks and nuns to practise and teach the Dharma, while it is the job of lay men and women to practise the Five Precepts and support the monks and nuns by providing them with their needs. This is an incorrect and dangerous belief, and in countries where it is widely accepted it has helped lead to a corruption of the Dharma.
The Buddha’s goal was to develop a community of disciples, ordained and lay, men and women, who were well-educated in the Dharma, who practised it fully, and who taught it to and learned it from each other. (D,II:104) While the Buddha praised Anathapindika [the lay Buddhist] for his great generosity, he reserved his highest praise for [his lay Buddhist disciples] Citta of Macchikasanda and Hatthaka of Alavi because they were both skilful in and diligent at giving something infinitely more precious than material things – the Dharma. (A,I:26)
Citta was the model Buddhist layman whose learning and behaviour the Buddha urged others to emulate. On one occasion, the Buddha said to the monks: “Should a devoted mother wish to encourage her beloved only son in a proper way she should say to him: ‘Try to become like the disciple Citta and the disciple Hatthaka of Alavi.'” (A,I:88)’
To further answer the question, it should be noted that both in and after the Buddha’s time, there are renown lay Buddhist teachers worldwide in all Buddhist traditions. There are also many Buddhist Sunday schools for children, classes for adults, and academic courses in universities (some of which offer Dharma education for monastics) led by lay Buddhist teachers. There are also leading teachers, who are recognised as Tulkus and Rinpoches in some Tibetan Buddhist traditions, who are not monastics as well. There are also monastics who become lay Buddhist teachers, and lay teachers who become monastics. What matters is that the Dharma is taught well.
The Buddha’s Lay Disciple Foremost In Teaching The Dharma