As with most fertility treatments, egg freezing faces its share of ethical objections from religious, cultural and individual standards. Whether or not you personally agree with the ethical implications, it's important that you're aware of what causes others to pause so that you can make an informed decision as to whether or not this fertility treatment is right for you.
Human Interference in Fertility
The most frequent and overarching objection against egg freezing, and most--if not all--fertility treatments, is that it puts human and scientific interference in the process. Even if some people make exceptions for those who struggle with infertility issues, freezing your eggs is not always a procedure undertaken only by those with infertility issues. You may choose to undergo this procedure despite not currently having any infertility issues in the hopes of not having to deal with infertility problems in the future.
The "Convenience" Factor
Many, but not all, of the people who object to egg freezing may only be objecting to the procedure when it's performed by women who are healthy. They may see the point of women who are undergoing chemotherapy, for example, to freeze their eggs prior to undergoing the procedure, but they may not like the idea of women who are healthy now but who want to delay pregnancy purely for the convenience of it freezing their eggs. They may object morally to the fact that women are trying to manipulate their childrearing to a more "convenient" time.
A counter-argument, of course, is that all methods of birth control act in a similar fashion--delaying pregnancy until the woman (or couple) feel that they're ready. However, freezing your eggs will take that birth control a step further because you're counting on keeping your younger, more plentiful eggs for a time when your eggs may not be as healthy or numerous. Just be aware that freezing one's eggs does not guarantee a decrease in birth defects or an increase in fertility at a later age. However, nor does the evidence suggest that it increases birth defects or is any less effective than having fertility treatments performed on eggs freshly harvested.
Perhaps less of an ethical implication than for a similar procedure like embryo freezing, but an objection even for egg freezing nonetheless, is that freezing your eggs is somewhat like "selecting" the "good" children from the "bad." In other words, you're freezing this healthy eggs now and opting to ignore the natural eggs you may produce at a later age. Also, not all of the eggs you freeze will become fertilized, so your fertility specialist will be discarding some of the eggs that seem less likely to succeed, i.e., discarding the "poorer" choices.
Other people's objections to egg freezing shouldn't stop you from considering the procedure, so long as you're aware of their points of view and you've made an informed, thought-out decision.