One of Islamic morality is never cut the others talk. Let them finish their talk, then you can talk after.
The Prophet sallallaahu ‘alaihi wasallam said:
إذا قلتَ للناسِ أَنصِتوا و هم يتكلَّمون ، فقد ألْغَيْتَ على نفسِك
“If you say ‘shut up’ to the people while they are talking, you’re really reproaching yourself” (HR Ahmad 2/318, Al Albani said this hadith is sahih [Silsilah Ash Shahihah, 1/328]).
This hadith originally tells us about the prohibition of speaking when khatib performing Friday khutbah.
But Shaikh Muhammad Nashiruddin Al Albani says:
“In this hadith, there is also a warning against the lack of the application of adab (moral). This adab is good in speaking and talking with people. That is, someone should not cut off the conversation of others when they are talking, he should silence and wait for them to finish speaking, even though he is a figure in his people. After they finish talking, then it is his turn to speak if he wants.
With this manner, someone will gather more informations from the words spoken. In order to discuss the problem between the two parties. Even more so when discussing about Islamic knowledge. But it is very unfortunate that many people discuss a problem they forgot about this behaviour. They should give a big attention to this good behaviour, which the Prophet Sallallahu’alaihi Wasallam taught us”
(Silsilah Al Ahadits As Sahihah, 1/329).