King James I England opposed the Presbyterian model as King of England. However, the system came from Scotland, where James was also king. Why did he accept the model in one country and deny it in another?
Largely because when he acceded to the English throne, and then de facto was assumed as Supreme Governor (or head) of the Church of England he was rather impressed with the Anglicans' polity.
This might've been compounded by the fact that Presbyterians had a certain visceral dislike of his mother - Mary, Queen of Scots and he wholly didn't approve of the Scottish reformation, which led eventually to the formalisation of Presbyterian ecclesiastical government by Andrew Melville and others. James I had the problem of Puritans in the Church of England that he came into conflict with, and he had associated them with the notoriously dour and ruthless Presbyterians in Scotland. This was not an entirely unreasonable equivocation either. Jasper Ridley's biography of John Knox touches on the fact that it's a fair assessment to say that the revolutionary spirit of the Puritans was obtained from that of Knox and others in the Scottish reformation.
These are really the two main factors: Pre-judged prejudices from his upbringing and reign in Scotland about the way Presbyterians in Scotland conducted themselves in political and religious affairs and exposure to an alternative system of church government when he became King of England.