The issue here is that you are pulling out into a stream of traffic and you shouldn't really do it. You say that none of the traffic in lane 3 was signalling that they wanted to go into lane 2, but it's a common mis-conception that you have to indicate left to move left. In this instance, traffic could have been indicating left to turn left (you don't say if the side road you were in was a one way traffic road) and this would have caused confusion. Even if it was a one way traffic road, so not an option for traffic to turn into, indicating left could be mistaken by traffic attempting to turn out into the 3 lane road.
The rule of thumb on ANY road is that you use lane 1 unless overtaking, or the lane takes you in a direction you don't want to go. If you are overtaking, you then use lane 2 and then the same rule as above applies - if lane 2 takes you in a direction you don't want to go, then move out to lane 3, or use lane three to overtake further traffic.
You said you were indicating (to turn left?) - how could traffic approaching from your right see this? You also make reference to 'my lane' - do you mean lane 2 on the main road? If so, it's not your lane: you are waiting on a side road and it is the lane of the approaching traffic. The only lane that is yours is the one you are in at the time - so this would be lane 1 on the side road.
In this instance, you shouldn't pull out into the road, as you're pulling out into oncoming traffic who may be wanting to revert back to lane 2 and have every right to do so, without indicating. It'll be this reason why the motorcyclist has seen fit to 'have a go'. Motorcyclists tend to go on the offensive because in the event of an accident, they come off worse, often through no fault of their own.