Can anybody tell me in simple words the major objections to the Cyclical Argument in Plato's Phaedo ?

The following extract from Michael Pakaluk might help though it will probably need more than one reading (just speaking from experience) :

The Cyclical Argument (CA) is not unfairly presented as follows:

1. Anything that comes to take on an attribute which has an opposite,
   previously had that opposite attribute.




2. Being dead and being alive are opposite attributes.




3. When something comes to be alive, it comes to take on the attribute
   of being alive.




4. Therefore, anything that comes to be alive previously had the attribute
   of being dead.




5. But everything that is dead was previously alive.




6. Therefore, anything that comes to be alive was previously alive.




7. Therefore, living things come from previously living things.




8. Therefore, living things will once again become living things.




9. Nothing comes to take on again, at a later time, an attribute that it
   now has, if it perishes in the process.




10. Thus, living things do not perish when they come to be dead, and in
    this sense they are immortal.

Plato's strategy is to connect this present life of a living thing with a previous life; that done, he draws the general conclusion that living things
were previously alive; yet, he reasons, they could not have come alive
again, if they did not endure in the interval between their previous life
and their current one; and thus, as regards any living thing, we can have
some confidence that it will continue to endure, in the interval after this
current life and before its next life.

Thus stated, the argument is clearly unsound, because the first premise
is in need of two familiar qualifications. That 'opposites come from opposites' is true only if: (i) we presume that we are not dealing with a case
of simple generation, where something comes to be F only in coming to
be simpliciter; and (ii) the opposites are 'contradictory', rather than mere
'contrary' opposites. But if premise 1. is qualified accordingly, premise 2.
needs to be revised: being dead and being alive are not contradictory
opposites, since there are things that are neither dead nor afive. Yet if we
rewrite premise 2., so that it involves opposites that are properly contradictory, e.g. 'Being not alive and being alive are opposite attributes', then
premise 5. needs to be changed accordingly, becoming: 'Everything that
is not alive was previously alive' - which is evidently false.

It would be good to have a diagnosis of why the argument goes wrong,
and for this purpose Gallop's commentary is particularly useful. Gallop
correctly notes, for instance, that Plato in CA tends to speak as though it
is the soul which comes to be alive, rather than the animal, but - Gallop
objects - this "insinuates a view of 'birth' in which the soul's discarnate
existence is already covertly assumed. And since that is precisely what
the argument purports to prove, the very conception of incarnation can be
seen to beg the essential question" (105). Again, Gallop wonders why we
shouldn't understand 'being dead' (in our premise 2. above) to mean, simply, 'ceasing to exist', in which case, clearly, 'being alive' and 'being
dead' could not be treated as opposing predicates, as CA requires, since
one would, in that case, be treating existence as though it were a predicate. Speculating on why Plato might have resisted this identification, Gallop
remarks that "a wedge might be driven between 'being dead' and 'ceasing to exist' by treating Socrates' soul as a separate subject, distinct from
Socrates himself, and alternating between incarnate and discarmate states.
But this would be, once again, to assume what has to be proved" (106).
Again, objecting to (our) premise 3. above, Gallop remarks that "The
sense of 'coming to be alive' required for the argument is not that in
which a living thing comes into being, but that in which a soul 'becomes
incarnate' in a living body. Yet it cannot do this unless it already exists
before birth or conception. And whether it does so or not is just what is
at issue" (110).

So Gallop maintains that CA goes awry because Plato begs the question, surreptitiously supposing that the soul is a distinct subject, independent of the body.

References

Michael Pakaluk, 'Degrees of Separation in the "Phaedo"', Phronesis, Vol. 48, No. 2 (2003), pp. 89-115: 90-2.

D. Gallop, Plato: Phaedo, Oxford: Clarendon Press, 1975.

C.J.F. Williams, 'On Dying', Philosophy 1969 (44) 217-30.