The possibilities of cloning embryos raise a number of ethical questions. Using embryonic cloning for reproductive purposes is questionable because the clone will be an identical replica of an existing person. This could be psychologically damaging for the clone -- especially if she is a clone of her mother! Further, creating a human from the genetic material of just one parent (rather than the combined genetic material of two parents) goes against the fundamental idea of conception as the joining of two individuals.
Cloning an embryo for the purposes of harvesting its cells is particularly controversial. The procedure involves creating an embryo, then using its cells to save a living human -- a process that necessarily destroys the embryo. The essential question is whether an embryo is considered "alive." If an embryo is categorized as a living human, killing it to harvest its stem cells for other purposes could be considered in some quarters as murder.
The word 'embryo' is also emotive as scientists are not using anything recognisable as human, but a collection of cells, no bigger than a punctuation mark, that are destroyed, usually after 6 days when it is at the blastocyst stage. Of course opponents argue that even this is wrong because a life has been started.