Learners learning at their own pace implies one cannot force learning one can only facilitate and provide an enabling environment

Pupils learning at their own pace implies that as a teacher one must consider the learning needs of the pupils and accord each one the needed facilitation so as to enable them learn while at the same time having the learner in mind when creating common activities, since others are fast learners and others are a bit slow.

Consciousness of learner centered lesson is the way to go now, any other thing is old fashioned

I love the Idea of the teacher playing the guide on the side role. This allows pupils, like plants, to flourish. In some institutions this idea is misunderstood to mean giving learners notes ti write...or asking them to make notes or doing lots of assignments ...

this means that the students in the same class are not the same and they have individual difference .Thus they do not learn at the same rate ,thus the teacher has to understand his/her students  and take them at the pace that best suite the students to ensure learning process takes place effectively

Sure!

Because Learner Centered education personalizes the learning, the voices of children are heard.

Pupils learning at their own pace, implies that teachers are expected to teach learners, all that they are required to know, in the course. They are to also help them develop and build good learning habits, that can help them function effectively, during their personal studies.