From what I know, people in Ireland started speaking English after the English conquest, but Scotland wasn't really conquered, so I started wondering when did Scotland start speaking English? Was it always the case?
Well the first English, or old English in this case, Speakers in what is today Scotland were Northumbrians, and Anglo Saxon Kingdom who's territory extended up the Firth of Forth on the east side of southern Scotland, expanding into this territory beginning around about 550. To their West was the Kingdom of Strathclyde whom were Brythonic speakers of the language of Cumbric. The closest modern language to which is Welsh, but this language is now extinct. To their north, particularly in the north east of Scotland was Pictland. The Pictish language was broadly speaking a celtic language and was probably more like Welsh than Gaelic but not as similar as Cumbric. Then in the North West of Scotland the Kingdom of Dál Riata was a Gaelic kingdom with links across the Irish sea linguistically, they spoke Gaelic which over time began to branch into Scottish Gaelic with something of a continuum of linguistic change across the arc from the South of Ireland to the boarders of Dal Riata territory.
Over time Dal Riata became the kingdom of Alba and would steadily expand its territory to take over the territory over much of the modern territory of mainland Scotland. There was some level of cultural fusion with Pictish elites and Scoto-Gallic ones but in the long term in terms of languages it would be Scottish Gaelic that would win out. Strathclyde would also be conquered as was the northern part of Northumbria such that by 1100 main and Scotland was mostly in the hands of the Kingdom of Scotland by which time the Pictish language would be mostly gone and Cumbric would be dying out by 1200 for the most part.
But at the same time those Northumbrian Old English Speakers did mostly keep their language intact and with the reign of David I more Anglo-Norman influence would begin to enter Scotland via the Scoto-Norman Burghs and Knights. David had spend part of his childhood in England, had marriage connections with the Norman kings of England and wanted to increase the economic and military power of his kingdom when he came to the throne. He therefore offered mostly anglo-norman knights land in Scotland in return for military service as well as setting up special towns with certain privileges into which English merchants and the like could move into. This produced small centres dotted about the Scottish lowlands of middle english speaking people which he hoped could form centres for growing Scotland's market economy and production as well as provide protection for the borderlands during his wars with England during this period. This trend would continue on over time with French, Gallic and middle English all being spoken in the Scottish court.
This is also where we get Scots. Scots is the name for what some people consider a language and some a dialect of English produced by middle English speakers in Scotland. Here they were isolated from some linguistic changes that occurred to English further south while diverge in some of their own ways. Scots became one of the most common languages of the Scottish Lowlands while Scottish Gaelic was common in the Scottish Highlands.
Fast forwards to when James VI of Scotland also managed to become James I of England. The Stewarts had already primarily spoken Scots as opposed to Scottish French or Scottish Gaelic for the past few centuries. And now while it was a Scottish King who now sat on the English and Scottish throne England was still now where the King primarily held his court and England who was the more influential economically in particular. And so the nobles of low land Scotland started to speak in a way that was closer to the early modern English that was emerging (The kind of English Shakespeare spoke) than Scots was.
By the time of the acts of union came about that combined the crowns to for the united kingdom of great Britain social pressure was causing this to bleed down and out, such nobles of the highlands were more likely to speak in a mixture of Scottish English and people in the Scottish Lowlands in general were increasingly speaking Scottish English rather than Scots. Men like Burns would help to keep the Scots language from dying out through continuing to produce a Scots literary tradition in addition to places where Scots remained spoken conversationally.
Meanwhile in the highlands from the mid 1700s to mid 1800s the Highland Clearances helped drive Scottish Gaelic language to the point where as it is now it is a minority language. To put the matter in a perhaps overly simplified manner the Highland Clan system was breaking down and shifting towards landlordism, where the land owners less regarded themselves as the head of a broader kinship group but merely as land owners, this was particularly exasperated where land was sold to wealthy Englishmen. As a result they moved to try to make more profit from their land at the expense of the people who lived there. Many highlanders, particularly from a middle class of famers that was being pressured out of existence, would end up emigrating as common land and traditional land rights and usage was undermined. Particularly as the potato famine hit the highlands in the hungry 40s resulting in both starvation and emigration. Combine this then with high rent and the top end land owners increasingly speak Gaelic less and less, the middle class of Gaelic farmers is being pushed out of existence one way or another and so the cultural weight on the remaining tenants means that they steadily end up speaking Scottish Gaelic less and less. While the economic situation would somewhat stablise eventually Scottish Gaelic has been increasingly been spoken less and less over time.